Geometry Complete Unit 2 - High School Math Teachers€¦ · Unit 2 Lesson Plans Name _____ HighSchoolMathTeachers.com©2020 Page 6 Unit: Unit 2 Angles and Lines Course: Geometry

Complete Unit 2

Package

HighSchoolMathTeachers.com©2020

Table of Contents

Unit 2 Pacing Chart -------------------------------------------------------------------------------------------- 1

Geometry Unit 2 Skills List ---------------------------------------------------------------------------------------- 5

Unit 2 Lesson Plans -------------------------------------------------------------------------------------------- 6

Day 16 Bellringer -------------------------------------------------------------------------------------------- 33

Day 16 Activity -------------------------------------------------------------------------------------------- 35

Day 16 Practice -------------------------------------------------------------------------------------------- 38

Day 16 Exit Slip -------------------------------------------------------------------------------------------- 43

Day 17 Bellringer -------------------------------------------------------------------------------------------- 45

Day 17 Activity -------------------------------------------------------------------------------------------- 47

Day 17 Practice -------------------------------------------------------------------------------------------- 49

Day 17 Exit Slip -------------------------------------------------------------------------------------------- 55

Day 18 Bellringer -------------------------------------------------------------------------------------------- 57

Day 18 Activity -------------------------------------------------------------------------------------------- 60

Day 18 Practice -------------------------------------------------------------------------------------------- 63

Day 18 Exit Slip -------------------------------------------------------------------------------------------- 70

Day 19 Bellringer -------------------------------------------------------------------------------------------- 72

Day 19 Activity -------------------------------------------------------------------------------------------- 75

Day 19 Practice -------------------------------------------------------------------------------------------- 78

Day 19 Exit Slip -------------------------------------------------------------------------------------------- 85

Week 4 Assessment -------------------------------------------------------------------------------------------- 87

Day 21 Bellringer -------------------------------------------------------------------------------------------- 94

Day 21 Activity -------------------------------------------------------------------------------------------- 96

Day 21 Practice -------------------------------------------------------------------------------------------- 98

Day 21 Exit Slip -------------------------------------------------------------------------------------------- 103

Day 22 Bellringer -------------------------------------------------------------------------------------------- 105

Day 22 Activity -------------------------------------------------------------------------------------------- 108

Day 22 Practice -------------------------------------------------------------------------------------------- 111

Day 22 Exit Slip -------------------------------------------------------------------------------------------- 116

Day 23 Bellringer -------------------------------------------------------------------------------------------- 118

Day 23 Activity -------------------------------------------------------------------------------------------- 120

Day 23 Practice -------------------------------------------------------------------------------------------- 122

Day 23 Exit Slip -------------------------------------------------------------------------------------------- 126

Day 24 Bellringer -------------------------------------------------------------------------------------------- 128

Day 24 Activity -------------------------------------------------------------------------------------------- 130

Day 24 Practice -------------------------------------------------------------------------------------------- 133

Day 24 Exit Slip -------------------------------------------------------------------------------------------- 136

Week 5 Assessment -------------------------------------------------------------------------------------------- 138

Day 26 Bellringer -------------------------------------------------------------------------------------------- 145

Day 26 Activity -------------------------------------------------------------------------------------------- 148

Day 26 Practice -------------------------------------------------------------------------------------------- 151

Day 26 Exit Slip -------------------------------------------------------------------------------------------- 155

Day 27 Bellringer -------------------------------------------------------------------------------------------- 157

Day 27 Activity -------------------------------------------------------------------------------------------- 159

Day 27 Practice -------------------------------------------------------------------------------------------- 162

Day 27 Exit Slip -------------------------------------------------------------------------------------------- 165

Day 28 Bellringer -------------------------------------------------------------------------------------------- 167

Day 28 Activity -------------------------------------------------------------------------------------------- 169

Day 28 Practice -------------------------------------------------------------------------------------------- 172

Day 28 Exit Slip -------------------------------------------------------------------------------------------- 175

Day 29 Bellringer -------------------------------------------------------------------------------------------- 177

Day 29 Activity -------------------------------------------------------------------------------------------- 179

Day 29 Practice -------------------------------------------------------------------------------------------- 182

Day 29 Exit Slip -------------------------------------------------------------------------------------------- 185

Week 6 Assessment -------------------------------------------------------------------------------------------- 187

Unit 2 Test -------------------------------------------------------------------------------------------- 196

Unit 2 Pacing Chart

HighSchoolMathTeachers.com ©2020 Page 1

Unit Week Day CCSS Standards Objective I Can Statements

Unit 2 Angles

and Lines

Week 4 – Algebraic

Definitions 16

CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment, based on the undefined notions of point, line, distance along a line, and

distance around a circular arc.

Know precise algebraic definitions of angle; complementary, supplementary

angles and angles on a straight line

I can give the precise algebraic definitions

complementary, supplementary angles and

angles on a straight line

Unit 2 Angles

and Lines


Definitions 17




Know precise algebraic definitions of angle; angles at a point

I can give precise algebraic definitions of angle at a

point

Unit 2 Angles

and Lines


Definitions 18




Know precise algebraic definitions of angle; Corresponding and alternate

angles

I can give algebraic definitions of

corresponding and alternate angles

Unit 2 Angles

and Lines


Definitions 19




Know precise algebraic definitions of angle; vertical and interior angles

I can give the precise algebraic definitions of

vertical and interior angles

Unit 2 Pacing Chart


Unit 2 Angles

and Lines


Definitions 20 Assessment Assessment Assessment

Unit 2 Angles

and Lines

Week 5 – Prove Geometric Theorems

21

CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.

Theorems include: vertical angles are congruent; when a transversal crosses

parallel lines, alternate interior angles are congruent and corresponding angles are

congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Prove that vertical angles are congruent

I can prove that vertical angles are congruent

Unit 2 Angles

and Lines


22





Prove that alternate interior angles are congruent

I can prove that alternate interior angles are

congruent

Unit 2 Angles

and Lines


23





Prove that corresponding angles are congruent

I can prove that corresponding angles are

congruent

Unit 2 Pacing Chart


Unit 2 Angles

and Lines


24





Prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's

endpoints.

I can prove that points on a perpendicular bisector of a

line segment are exactly those equidistant from the

segment's endpoints.

Unit 2 Angles

and Lines


25 Assessment Assessment Assessment

Unit 2 Angles

and Lines

Week 6 – Prove Algebraically

26





Given an angle, use the algebraic properties to show that alternate, vertical and corresponding angles

among others are equal

Given an angle, I can use the algebraic properties to

show that alternate, vertical and corresponding angles among others are

equal

Unit 2 Angles

and Lines


27

CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and

perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given

line that passes through a given point).

Prove the slope criteria for parallel and perpendicular lines

I can prove the slope criteria for parallel and

perpendicular lines

Unit 2 Pacing Chart


Unit 2 Angles

and Lines


28

CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and

perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given


Use slope criteria to solve geometric problems (e.g., find the equation of a

line parallel or perpendicular to a given line that passes through a given point).

I can use slope criteria to solve geometric problems (e.g., finding the equation

of a line parallel or perpendicular to a given


Unit 2 Angles

and Lines


29

CCSS.MATH.CONTENT.HSG.GPE.B.6 Find the point on a directed line segment

between two given points that partitions the segment in a given ratio.

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

I can find the point on a directed line segment

between two given points that partitions the segment

in a given ratio.

Unit 2 Angles

and Lines


30 Assessment Assessment Assessment

Geometry Unit 2 Skills List Name ____________________________________

HighSchoolMathTeachers.com©2020 Page 5

Geometry Unit 2 Skills List

Number Unit CCSS Skill

8 2 HSG.CO.C.9 Prove theorems about lines and

angles

9 2 HSG.GPE.B.5 Prove the slope criteria for parallel

and perpendicular lines

10 2 HSG.GPE.B.5

Use the slope criteria for parallel and

perpendicular lines to solve

geometric problems

11 2 HSG.GPE.B.6

Find the point on a directed line

segment that partitions the segment

in a given ratio

Unit 2 Lesson Plans Name ____________________________________


Unit: Unit 2 Angles and Lines

Course: Geometry

Topic: Week 4 – Algebraic Definitions

Day: 16

Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision.

Objective: Know precise algebraic definitions of angle; complementary, supplementary angles and angles on a straight line

I can statement: I can give the precise algebraic definitions complementary, supplementary angles and angles on a straight line

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will measure and identify supplementary and complementary angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.

Materials: Bellringer 16 Day 16 Activities Day 16 Practice Day 16 Presentation Day 16 Exit Slip



Accommodations/Special Circumstances:

Technology:

Reflection:

Extra/Additional Resources:




Course: Geometry


Day: 17



Objective: Know precise algebraic definitions of angle; angles at a point

I can statement: I can give precise algebraic definitions of angle at a point

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students will draw angles at a point then find out about their properties. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 18



Objective: Know precise algebraic definitions of angle; Corresponding and alternate angles

I can statement: I can give algebraic definitions of corresponding and alternate angles

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will measure and identify vertical and interior angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 19



Objective: Know precise algebraic definitions of angle; vertical and interior angles

I can statement: I can give the precise algebraic definitions of vertical and interior angles

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will measure and identify vertical and interior angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:





Course: Geometry


Day: 20

Common Core State Standard: Assessment

Mathematical Practice: Assessment

Objective: Assessment

I can statement: Assessment

Procedures: Assessment

Materials: Assessment


Technology:

Reflection:





Course: Geometry

Topic: Week 5 – Prove Geometric Theorems

Day: 21

Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

Objective: Prove that vertical angles are congruent

I can statement: I can prove that vertical angles are congruent

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The students will use thin metal bars,or straight wires to see tha changes in size of vertically opposite angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 22



Objective: Prove that alternate interior angles are congruent

I can statement: I can prove that alternate interior angles are congruent

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will use the concept of measuring to come upwith to prove the congruence of alternate interior angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 23



Objective: Prove that corresponding angles are congruent

I can statement: I can prove that corresponding angles are congruent

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will use the concept of measuring to come upwith to prove the congruence of corresponding angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 24



Objective: Prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

I can statement: I can prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 7. Students will prove the equality of the points on a perpendicular bisector to the end points of a line using a number of strings. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 25








Technology:

Reflection:





Course: Geometry

Topic: Week 6 – Prove Algebraically

Day: 26


Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Objective: Given an angle, use the algebraic properties to show that alternate, vertical and corresponding angles among others are equal

I can statement: Given an angle, I can use the algebraic properties to show that alternate, vertical and corresponding angles among others are equal

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will be able to verify that vertical angles are equal in preparation for the lesson 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 27

Common Core State Standard: CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).


Objective: Prove the slope criteria for parallel and perpendicular lines

I can statement: I can prove the slope criteria for parallel and perpendicular lines

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will work in groups of four to discover the slope criteria of parallel lines by drawing three parallel lines and comparing the steepness 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 28

Common Core State Standard: CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Objective: Use slope criteria to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

I can statement: I can use slope criteria to solve geometric problems (e.g., finding the equation of a line parallel or perpendicular to a given line that passes through a given point).

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.





Technology:

Reflection:





Course: Geometry


Day: 29

Common Core State Standard: CCSS.MATH.CONTENT.HSG.GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Objective: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

I can statement: I can find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will verify the formula for proportional division of a line. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.



Technology:



Reflection:


Day 16 Bellringer Name ____________________________________



Course: Geometry


Day: 30








Technology:

Reflection:




1. In the figure below identify the following types of angles:

(a) an acute angle

(b) an obtuse angle

(c) a right angle

(d) a straight angle

2. Name the angle represented below in four different ways.

3. Solve for the unknown in the following equations:

(a) 4𝑥 − 20 = 160 − 6𝑥

(b) 𝑥 − 50 = 40 − 2𝑥

∅

K

L M

A

B

C

D

E

O



Answer Keys

Day 16:

1. (a) ∠AOB, ∠BOC, ∠COD, ∠DOE

(b) ∠AOD, ∠BOE

(c) ∠AOC,∠COE

(d) ∠ AOE

2. ∠L, ∠KLM, ∠MLK, ∠∅

3. (a) 𝑥 = 18

(b) 𝑥 = 30

Day 16 Activity Name ____________________________________


A

B

1. Measure angle AOB using a protractor and write down the angle measure.

2. Measure angle BOC and write down the angle measure.

3. Find the sum of angle AOB and angle BOC. Write down the sum.

A O

B

C

D

P

O R

Q



4. Now measure angle AOC along line AC and compare the angle measure to the sum you got in 3 above.

What do you notice?

5. Similarly, measure angle AOD and angle COD and note down the two angle measures.

6. Find the sum of angle AOD and angle COD. Write down the sum. Compare this sum to the angle

measure AOC.

7. What can you say about the sum of angles along line AC after measuring the two angles above the

line and the two angles below the line?

8. Measure angle POQ and write down its measure.

9. Measure angle QOR and write down its measure.

10. Find the sum of angles POQ and QOR and write it down.

11. Now, measure angle POR and write down its measure. Compare the sum in 10 above and the

measure of angle POR. What do you notice?



In this activity, students will discover complementary angles, supplementary angles and angles on a

straight line on their own. You will design a pair of angles accurately on two different A4 papers. One

paper labeled A containing a set of complementary angles and the other paper labeled B containing a

set of supplementary angles as shown below. You will be obliged to walk around the groups and assist

the students where necessary, especially in measuring the angles. Students will work on the activity in

groups of 4, and each group will require a protractor and two A4 papers, containing the two sets.

Answer Keys

Day 16:

1. The angles from all the pairs should be similar.


3. The angle sum should be 180°

4. The sum is equal to angle AOC


6. The sum is equal to angle AOC

7. Their sum is 180°



10. Their sum is 90°

11. They are equal

Day 16 Practice Name ____________________________________


Find the supplements of the angles in questions 1-5:

1. 67°

2. 111°

3. 44°

4. 57°

5.179°

Find the complements of the angles in questions 6-10

6. 89°

7. 23°

8. 66°

9. 1°

10. 90°



11. The angle measure of a supplement of an angle is 12° more than twice the angle. Calculate the

measure of the two angles.

12. The angle measure of a complement of an angle is 4° more than thrice the angle. Calculate the

measure of the two angles.

Find the value of 𝑥 in the figures in questions 13-16. (Angles not drawn to scale)

13.

14.

15.

𝑥 + 20°

40° 60°

7𝑥

2𝑥 3𝑥

2𝑥 − 30°

3𝑥 + 60° 10°



16.

In questions 17 and 18, identify whether the sum of the angle shown and the unknown angle is

supplementary or complementary.

17.

18.

𝑥 + 45°

𝑥 − 10° 3𝑥 − 60°

115° 𝑥

31°

𝑥



Use the figure below to answer questions 19 and 20.

19. Identify two supplements of ∠𝑇𝑂𝑈

20. Identify a pair of complementary angles.

R

P O S

Q

T

U



Answer keys

Day 16:

1. 113°

2. 69°

3. 136°

4. 123°

5. 1°

6. 1°

7. 67°

8. 24°

9. 89°

10. 0°

11. 56° 𝑎𝑛𝑑 24°

12. 68.5° 𝑎𝑛𝑑 21.5°

13. 𝑥 = 60°

14. 𝑥 = 15°

15. 𝑥 = 28°

16. 𝑥 = 41°

17. Supplementary

18. Complementary

19. ∠𝑄𝑂𝑈 𝑎𝑛𝑑 ∠𝑅𝑂𝑇

20. ∠𝑃𝑂𝑄 𝑎𝑛𝑑 ∠𝑄𝑂𝑅

Day 16 Exit Slip Name ____________________________________


1. (a) Find the supplement of 153°

(b) Find the complement of 49°

2. In a given pair of complementary angles, the size of the larger angle is four times the size of the

smaller angle. Find the size of the two angles.



Answer Keys

Day 16:

1. (a) 27°

(b) 41°

2. 72° and 18°



1. What is the value of b given that AB is a straight line?

2. Use the figure below to answer the questions that follow.

a) What is the value of c?

b) What is the value of d?

3. a) If a and b are complementary angles and the value of a is 49°, what is the values of b?

b) If c and d are two supplementary angles and the value of d is 300, what is the value of c?

A B

b 600

c d 390



Answer Key Day 17

1. 120°

2. a). 51°

b).90°

3. a).41°

4. b).150°



1. Draw a straight line on a plain paper using a ruler and a pencil and mark any point on the line and

label it T.

2. Draw other two lines through point T as shown below.

3. Measure each angle at point T using a protractor and record their values.

4. Add the angles on one side of each straight line; what is their sum in each case?

5. Add the values you got in step 3. What is their sum?

T

T



In this activity, we are required to draw a line and identify a fixed point in that line then draw other lines

through that point. Students are required to divide themselves into groups of at least three. Each group

is required to have a plain paper, a pencil, a ruler and a protractor.

Answer Keys

Day 17:

1-3. No response

4. 180°

5. 360°



In questions 1- 7 find the angle marked by a letter:

1.

2.

3.

4.

a

800 870

230 c

960

1140 d

b

950 48



5.

6.

7.

8.

520 1360

1070

e

790 1500

950 f

1200 1000

800 h

830

g



9.

10.

Use the figure below to answer questions 11 – 13

11. What is the value of j?

12. What is the value of i?

13. Find the value of h.

720

h i

j

1330 1350

j

2740

470 i



14. Find the value of the angle marked l?

15.Find the angle k.

Use the fig below to answer questions 16, 17 and 18.

16. What is the value of m?

17. Find the value of n.

18. What is the value of o?

3330

l

870

930 124

0

k

m 580

n o



Use the figure below to answer questions 19 and 20.

Lines AB and CD are straight.

19. Find the value of r.

20. What is the value of s?

1180

540

A

B C

D

r s



Answer Key

Day 14.

1. 90°

2. 217°

3.170°

4. 150°

5. 65°

6. 36°

7. 277°

8. 60°

9. 39°

10. 92°

11. 108°

12. 72°

13. 108°

14. 27°

15. 56°

16. 90°

17. 32°

18. 90°

19. 62°

20. 64°



1. Find the value of angle a in the figure below.

1300

a 800

1000



Answer Keys

Day 1:

1. 500



1. Find the value of a in the diagrams below.

(a)

(b)

(c)

𝑎 + 10°

57° 72°

2𝑏 + 31° 44°

89°

3𝑐 + 42° 5𝑐 − 64°

42°



2. Find the angle measure represented by the letter in each case.

(a)

(b)

112°

3𝑦

𝑦

2𝑦

2𝑦

140° 13𝑡

7𝑡

11𝑡

9𝑡



Answer Keys

Day 18:

1. (a) 𝑎 = 41°

(b) 𝑏 = 8°

(c) 𝑐 = 20°

2.

(a) 𝑦 = 31°

(b) 𝑡 = 5.5°



1. Place the ruler on the paper and draw two lines of about 5 inches on either side of the ruler. The lines

should appear as shown below.

2. Remove the ruler and observe the lines you have drawn. What relationship exists between the two

lines?

3. Draw another straight line using a ruler to cut across the two lines as shown below.

4. Label the angles formed as shown below.

a b

c d

f e

g h



5. Using a protractor measure accurately each angle in the following pairs of angles: ∠𝑎 and ∠𝑒; ∠𝑐 and

∠𝑔; ∠𝑏 and ∠𝑓; ∠𝑑 and ∠ℎ .What do you notice about the measures of the angles in each pair?

6. Using a protractor measure each angle in the following pairs of angles: ∠𝑐 and ∠𝑓; ∠𝑑 and ∠𝑒. What

do you notice about the measure of the angles in each pair?

7. Using a protractor measure each angle in the following pairs of angles: ∠𝑎 and ∠ℎ; ∠𝑏 and ∠𝑔. What

do you notice about the angles in each pair?



In this activity, students will identify the relationship between angles formed when a line intersects a

pair of parallel lines. Students will work in groups of 4. Each group will require a ruler with straight

edges, a protractor, a pencil and a plain paper.

Answer Keys Day 18:

1. No response

2. They are parallel

3. The line must be drawn using a ruler, and it must intersect the two lines.

4. No response

5. Different responses; the pairs are approximately equal





In questions 1-5, find the alternate interior and alternate exterior angles represented by letters. The two

lines shown in each case are parallel.

1.

2.

3.

105°

𝑥 𝑦

51°

𝑥 𝑦

123°

𝑥

𝑦



4.

5.

66°

𝑥 𝑦

109°

𝑥

𝑦



Given that 𝐴𝐵⃗⃗⃗⃗ ⃗ is parallel to 𝐶𝐷⃗⃗⃗⃗ ⃗ and line q is parallel to line r. Use the diagram to answer questions 6-10.

t is in degrees.

6. Find the value of t if ∠4 = 2𝑡 + 8 and ∠8 = 80°.

7. Find the value of t if ∠1 = 3𝑡 − 12 and ∠12 = 60°

8. Find the value of t if ∠7 = 𝑡 − 15 and ∠14 = 45 − 2𝑡

9. Find the value of t if ∠1 = 5𝑡 − 10 and ∠9 = 2𝑡 + 50

10. Find the value of t if ∠6 = 20𝑡 − 4 and ∠15 = 10𝑡 + 16

q r

1 2

3 4

5 6

7 8

9 10

11 12

13 14

15 16



In questions 11-15, calculate the value of y that makes 𝑁𝑃⃗⃗⃗⃗⃗⃗ is parallel to 𝑄𝑅⃗⃗ ⃗⃗ ⃗⃗ . The value of y is in degrees.

11.

12.

13.

Q 100° − 2𝑦

𝑦 − 20° N P

R

Q

60°

5𝑦 + 10°

N P

R

Q 80°

2𝑦 − 24°

N P

R



14.

15.

If QR and ST are parallel, identify whether the angles in questions 16-19 in the figure below are

corresponding, alternate interior or alternate exterior angles.

Q

140°

2𝑦 + 60° N P

R

Q

140°

𝑦 + 30°

N P

R

1 2

3 4

5 6

7 8

Q

R

S

T



16. ∠2 and ∠7

17. ∠3 and ∠6

18. ∠2 and ∠6

19. ∠3 and ∠7

20. Identify all congruent angles from the figure above.



Answer keys

Day 18:

1. 𝑥 = 105°, 𝑦 = 75°

2. 𝑥 = 51°, 𝑦 = 129°

3. 𝑥 = 123°, 𝑦 = 57°

4. 𝑥 = 114°, 𝑦 = 66°

5. 𝑥 = 109°, 𝑦 = 71°

6. 𝑡 = 36°

7. 𝑡 = 24°

8. 𝑡 = 20°

9. 𝑡 = 20°

10. 𝑡 = 2°

11. 𝑦 = 22°

12. 𝑦 = 62°

13. 𝑦 = 40°

14. 𝑦 = 40°

15. 𝑦 = 110°

16. Alternate interior

17. Alternate exterior

18. Corresponding

19. Corresponding

20. ∠1 ≅ ∠5; ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠4 ≅ ∠8; ∠2 ≅ ∠7; ∠4 ≅ ∠5; ∠1 ≅ ∠8; ∠3 ≅ ∠6



Calculate the size of the angles represented by letters on the diagram below. (Angles not drawn to scale)

123° 𝑥

𝑦 𝑧

72°



Answer Keys

Day 18:

𝑥 = 57°, 𝑦 = 57°, 𝑧 = 108°



1. Find the alternate interior and alternate exterior angles represented by letters. The two lines shown

in each case are parallel.

(a)

(b)

54° 126°

𝑥 𝑦

27°

153°

𝑥

𝑦



(c)

2. Using your angle values in question 1(b) above, find the following sums:

(a) 153° + 𝑦

(b) 𝑥 + 27°



Answer Keys

Day 19:

1. (a) 𝑥 = 126°, 𝑦 = 54°

(b) 𝑥 = 153°, 𝑦 = 27°

(c) 𝑥 = 33°, 𝑦 = 147°

2. (a) 180°

(b) 180°



1. Place the ruler on the paper and draw two lines of about 5 inches on either side of the ruler.

2. Remove the ruler and draw another straight line using a ruler to cut across the two lines as shown

below.

3. Label the angles formed as shown below.

a b

c d

f e

g h



4. Compare the positions of the following angles relative to each other: ∠𝑎 and ∠𝑑; ∠𝑏 and ∠𝑐; ∠𝑒 and

∠ℎ; ∠𝑓 and ∠𝑔. What do you notice about these positions?

5. Using a protractor measure accurately each angle in the following pairs of angles: ∠𝑎 and ∠𝑑; ∠𝑏 and

∠𝑐; ∠𝑒 and ∠ℎ; ∠𝑓 and ∠𝑔. What do you notice about the measure of one angle compared to the other

in these pairs ?

6. Using a protractor measure each angle in the two pairs of angles: ∠𝑑 and ∠𝑓; ∠𝑐 and ∠𝑒.

7. Now, find the sum of the angles in those pairs as ∠𝑑 + ∠𝑓 and ∠𝑐 + ∠𝑒. What is common about the

two sums.



In this activity, students will discover some key properties of vertical and interior angles. Students will

work in groups of 4. Each group will require a ruler with straight edges, a protractor, a pencil and a plain

paper.

Answer Keys Day 19:

1. No response

2. No response

3. No response

4. The angles are opposite each other

5. Responses will differ on each angle measured; In each pair, the angles are equal

6. Responses will differ

7. They all add up to 180°



In questions 1-5, find the value of the angle represented by the letters.

1.

2.

3.

𝑧 67°

t 59°

𝑎

77°



4.

5.

In questions 6-10, find the value of the angle represented by the letter. In each case, the two lines

intersected by the transversal are parallel.

6.

ℎ 167°

𝑟

171°

x

127°



7.

8.

9.

10.

y

118°

t

59°

d

103°

g

67°



In questions 11-15, solve for x in the given figures. The two lines intersected by the transversal are

parallel.

11.

12.

13.

14.

ሺ𝑥 + 30ሻ°

119°

ሺ2𝑥 − 7ሻ°

ሺ4𝑥 − 11ሻ°

ሺ𝑥 − 60ሻ°

ሺ4𝑥 − 20ሻ°

ሺ5𝑥 − 14ሻ°

ሺ3𝑥 + 6ሻ°



15.

Find the value of x and hence angle ∠AOB in questions 16-20.

16.

17.

ሺ40𝑥 − 4ሻ°

ሺ10𝑥 − 16ሻ°

A

O

B

ሺ𝑥 + 29ሻ°

ሺ2𝑥 − 9ሻ°

A

O B ሺ2𝑥 + 8ሻ°

ሺ𝑥 + 21ሻ°



18.

19.

20.

A

O

B

ሺ3𝑥 + 21ሻ°

ሺ𝑥 + 63ሻ°



Answer keys Day 19:

1. 𝑧 = 67°

2. 𝑡 = 59°

3. 𝑎 = 77°

4. ℎ = 167°

5. 𝑧 = 171°

6. 𝑥 = 53°

7. 𝑦 = 62°

8. 𝑡 = 121°

9. 𝑑 = 77°

10. 𝑔 = 113°

11. 𝑥 = 31°

12. 𝑥 = 33 °

13. 𝑥 = 52°

14. 𝑥 = 23.5°

15. 𝑥 = 4°

16. 𝑥 = 38°

∠𝐴𝑂𝐵 = 67°

17. 𝑥 = 13°

∠𝐴𝑂𝐵 = 146°

18. 𝑥 = 40°

∠𝐴𝑂𝐵 = 80°

19. 𝑥 = 21°

∠𝐴𝑂𝐵 = 84°

20. 𝑥 = 79°

∠𝐴𝑂𝐵 = 110°



In the figure below, KM⃗⃗⃗⃗⃗⃗ and LN⃗⃗⃗⃗ ⃗ intersect at O.

(a) Find the value of y.

(b) Hence, find :

(i) ∠NOM

(ii) ∠KOL

ሺ𝑦 + 69ሻ°

ሺ2𝑦 + 2ሻ°

K

L

M

N

O



Answer Keys

Day 19:

(a) 𝑦 = 67

(b) 35°

(c) 35°

87

High School Math Teachers

Geometry

Week 4 Assessment

©2020HighSchoolMathTeachers

88

Week 4

Weekly Assessments

89

Week #4 1. Identify the transformation involved in each case. a)

b)

2. Find the value of the angle marked with a letter. a) b)

3. Use the diagram below to answer the following questions. a) Which rigid motion maps the triangles above onto each other? b) Are the two triangles congruent?

4. Use the figure below to answer the questions that follow. a) Which angle forms alternate angles with 𝑘? b) Which angle forms corresponding angles with 𝑗?

88°

𝑎

𝑏 73° 130°

53°

𝑓 𝑒 𝑔

ℎ

𝑖 𝑗 𝑘

𝑙

90

5. 𝑎 and 𝑏 are supplementary angles. 𝑏 − 36 = 131°. a) Find the value of 𝑎. b) Find the value of 𝑏.

6. State whether the following figures are congruent. a) b)

91

Week 4 - KEYS

Weekly Assessments

92

Week #4 KEY 1. Identify the transformation involved in each case. a) Reflection

b) Translation

2. Find the value of the angle marked with a letter. a) 272° b) 49°

3. Use the diagram below to answer the following questions. a) Which rigid motion maps the triangles above onto each other? Translation b) Are the two triangles congruent? Yes

4. Use the figure below to answer the questions that follow. a) Which angle forms alternate angles with 𝑘? 𝑓 b) Which angle forms corresponding angles with 𝑗? 𝑒

88°

𝑎

𝑏 73° 130°

53°

𝑓 𝑒 𝑔

ℎ

𝑖 𝑗 𝑘

𝑙

93

5. 𝑎 and 𝑏 are supplementary angles. 𝑏 − 36 = 131°. a) Find the value of 𝑎. 13° b) Find the value of 𝑏.

167°

6. State whether the following figures are congruent. a) They are congruent b) They are not congruent



1. Use the figure below to answer the questions that follow.

If DF and EG are straight lines and ∠𝐷𝑂𝐸 = 113°;

a) What is the value of ∠𝐺𝑂𝐹?

b) What is the value of ∠𝐸𝑂𝐹?

c) What is the value of ∠𝐷𝑂𝐺?

2. What is the value of the angle marked a below given that AB is a straight line?

3. If b and c are two supplementary angles and the value of b is 41°, what is the value of c?

D E

G F

113°

O

64° a

A B



Answer Key Day 21.

1 a) 113°

b) 67°

c) 67°

2. 116°

3. 139°



1. Using the marker pen, mark an arbitrary point on each metal bar close to their centers.

2. Place one metal bar over the other such that the points you made touch each other as shown below.

3. Adjust the metal bars to different angles and observe how the opposite angles behave.

4. Adjust the metal bars until they make an obtuse angle.

5. Compare the size of in 4 above with the size of the angle opposite to it. Which kind of angle is it?

6. Adjust the metal bars to reduce the size of the obtuse angle and observe what happens to the angle

opposite to it as you reduce. What happens to the angle in the opposite direction?



In this activity, students are required to compare how the size of a vertical angle changes if the size of

the other vertical angle is changed. Students are required to divide themselves into groups of at least

three. Each group is required to have two thin metal bars and a marker pen.

Answer Keys

Day 21:

1-4. No response

5. The angle opposite to it is also an obtuse angle.

5. The opposite angle reduces its size.



In the figure below AB and CD are straight lines and ∠𝐴𝑂𝐶 = 710. Use the figure to answer questions 1

to 3.

1. What is the size of ∠𝐴𝑂𝐷?

2. What is the size of ∠𝐵𝑂𝐶?

3. Compare the sizes of ∠𝐴𝑂𝐷 and ∠𝐵𝑂𝐶.

Use the figure below to answer questions 4 to 6. CD and FG are straight lines.

4. Find ∠𝐶𝑂𝐹.

5. What is the size of ∠𝐷𝑂𝐺?

6. Compare the sizes of ∠𝐶𝑂𝐹 and ∠𝐷𝑂𝐺.

167∘ C

D F

G

O

A

O

B C

D

71°



Use the figure below to answer questions 7 to 9. HI and JK are straight lines which intersect at P.

7. Find ∠𝐼𝑃𝐽

8. What is the value of ∠𝐻𝑃𝐾?

9. Compare the sizes of ∠𝐼𝑃𝐽 and ∠𝐻𝑃𝐾

Use the figure below to answer questions 10 to 12. AB and CD are straight lines.

10. What is the value of the angle marked a?

90

H J

K I

P

A

B

C

D

a 37°

b



11. What is the value of the angle marked b?

12. Compare the size of a and that of b.

In the figure below ST and UV are straight lines which intersect at M. Use the figure to answer questions

13,14 and 15.

13. Find ∠𝑈𝑀𝑇

14. Find ∠𝑆𝑀𝑉

15. Compare the size of ∠𝑈𝑀𝑇 and that of ∠𝑆𝑀𝑉.

Use the figure below to answer questions 16,17 and 18. AD and FG are straight lines.

S

T

U

V

59°

M

89°

A

D F

G

O



16. Find ∠𝐴𝑂𝐹

17. Find ∠𝐷𝑂𝐺

18. Compare the sizes of ∠𝐴𝑂𝐹 and ∠𝐷𝑂𝐺

Use the figure below to answer questions 19 and 20. KL and MN are straight lines.

19. Find ∠𝐾𝑂𝑀 and ∠𝐿𝑂𝑁

20. Compare the two angles in 19 above.

147° K

L M

N

O



Answer Keys

Day 21:

1. 109°

2. 109°

3. They are equal

4. 13°

5. 13°

6. They are equal

7. 171°

8. 171°

9. They are equal

10. 143°

11. 143°

12. They are equal

13. 121°

14. 121°

15. They are equal

16. 91°

17. 91°

18. They are equal

19. ∠𝐾𝑂𝑀 = 33° and ∠𝐿𝑂𝑁 = 33°

20. They are equal



1. What is the relationship between the size of ∠𝐴𝑂𝐶 and the size of ∠𝐵𝑂𝐷 given that AB and CD are

straight lines.

B

A

C

D

O



Answer Keys

Day 22:

1. ∠𝐴𝑂𝐶 = ∠𝐵𝑂𝐷



1. Find the angles represented by letters in the figures below. In each case the two lines intersected by

the transversal are parallel.

(a)

(b)

(c)

57°

𝑥

66°

𝑦

136°

𝑧



2. Find the value of y in the figures below given that NP⃡⃗⃗⃗ ⃗ ∥ QR ⃡⃗ ⃗⃗⃗⃗ in each case.

(a)

(b)

Q

ሺ24𝑦 − 16ሻ°

ሺ20𝑦 + 4ሻ°

N P

R

Q

ሺ𝑦 + 48ሻ°

ሺ2𝑦 − 12ሻ°

N P

R



Answer Keys

Day 22:

1. (a) 𝑥 = 57°

(b) 𝑦 = 66°

(c) 𝑧 = 136°

2. (a) 𝑦 = 60°

(b) 𝑦 = 5°



1. Place the ruler on the paper and draw two parallel lines of about 3 inches on either side of the ruler.

2. Remove the ruler and draw a transversal to intersect the parallel lines as shown below.

3. Now, label four angles exactly as shown below.

a b

d c



4. What can you say about the position of the angles relative to the parallel lines?

5. Measure ∠𝑎 and ∠𝑑 accurately using a protractor. What do you notice about the measures of the two

angles?

6. Consider and note the position of ∠𝑎 relative to ∠𝑑.

7. Similarly, measure ∠𝑏 and ∠𝑐 accurately using a protractor. What do you notice about the measures

of the two angles?

8. Similarly, consider and note the position of ∠𝑏 relative to ∠𝑐.

9. Identify one key similarity between the two pairs of angles you have measured.



In this activity, students will be able to verify that alternate interior angles are equal. Students will work

on the activity in groups of four. Each group will be required to have a plain paper, a ruler graduated in

inches, a pencil and a protractor.

Answer Keys

Day 22:

1. No response

2. No response

3. No response

4. They are located between the parallel lines

5. The angles are equal

6. This is to remind the students about the position of a pair of alternate angles

7. The angles are equal

8. This is to remind the students about the position of a pair of alternate angles

9. Angles in each pair have equal measures



Use the parallelogram PQRS formed by the two pairs of parallel lines below to answer questions 1-5.

∠PQR = 77°.

1. Find ∠PQU

2. Find ∠QPS

3. Hence find ∠QPT

4. Compare ∠PQR to ∠QPT. What can you deduce about the measures of the two angles?

5. Similarly, compare ∠PQU to ∠QPS. What can you deduce from the measures of the two angles?

P

Q

S

R

77°

T

U



Use the figure below to answer questions 6-12.

6. Find the value of x

7. Find the actual measure of ∠QTX

8. Find the actual measure of ∠RXT

9. Find ∠PTX

10. Find ∠SXT

11. Compare ∠RXT to ∠QTX. What do you deduce from the measures of the two angles?

12. Compare ∠PTX to ∠SXT. What do you deduce from the measures of the two angles?

T

ሺ12𝑥 − 8ሻ°

ሺ10𝑥 + 2ሻ°

P

R

Q

S X



In the figure below, KL ∥ MN. The two pairs of parallel lines form parallelogram ABCD. ∠𝐵𝐴𝐷 = 61°.

13. Find ∠BAT

14. Find ∠ABC

15. Find ∠ABU

16. Compare ∠BAT to ∠ABC. What do you discover about the measures of the two angles?

17. Compare ∠ABU to ∠BAD. What do you discover about the measures of the two angles?

L

K M

N

A

B C

D

61°

T

U



In the figure below EF is a transversal and AB∥ CD.

18. Find the value of 𝑥.

19. Find the actual measure of ∠BEF and hence find ∠AEF. Similarly, find the actual measure of ∠DFE

and hence find ∠CFE.

20. Compare ∠AEF to ∠DFE and also compare ∠CFE to ∠BEF. How are the two angles in each case

related?

E

ሺ5𝑥 + 13ሻ°

ሺ7𝑥 − 37ሻ°

A

C

B

D F



Answer keys

Day 22:

1. ∠PQU = 103°

2. ∠QPS = 103°

3. ∠QPT = 77°

4. They have equal angle measures


6. 𝑥 = 5°

7. ∠QXT = 52°

8. ∠RXT = 52°

9. ∠PTX = 128°

10. ∠SXT = 128°



13. ∠BAT = 119°

14. ∠ABC = 119°

15. ∠ABU = 61°

16. They are equal

17. They are equal

18. 𝑥 = 17°

19. ∠BEF = 82°; ∠AEF = 98°; ∠DFE = 98°; ∠CFE = 82°

20. The angles are congruent



Use the parallelogram KLMN formed by the two pairs of parallel lines below to answer the questions

that follow. ∠LKN = 111°.

(1) Find ∠PKL

(2) Find ∠KLM and hence find ∠OLK

(3) Compare ∠PKL to ∠KLM. What can you deduce about the measures of the two angles?

(4) Similarly, compare ∠LKN to ∠OLK. What can you deduce about the measures of the two angles?

K

L

N

M

111°

P

O



Answer Keys

Day 22:

1. ∠PKL = 69°

2. ∠KLM = 69°

∠OLK = 111°

3. ∠PKL = ∠KLM.

4. ∠LKN = ∠OLK



Use the following diagram to answer the following questions

1. Write all pairs of corresponding angles

2. Write all pairs of supplementary angles sharing the same point

3. Write all pairs of supplementary angles that are not sharing the same point

4. Find the sum of angles 𝑚, 𝑥, 𝑝 and 𝑦.

5. Compare the sum of 𝑎 and 𝑟 and that of 𝑝 and 𝑥.

𝑎

𝑥 𝑦

𝑟

𝑚

𝑛

𝑝

𝑞



Answer Keys

Day 23:

1. 𝑟 and 𝑝; 𝑞 and 𝑦; 𝑎 and 𝑚; and 𝑛 and x

2. 𝑎 and 𝑟; 𝑟 and 𝑞, 𝑞 and 𝑛, 𝑛 and 𝑎, 𝑚 and 𝑝; 𝑝 and 𝑦, 𝑦 and 𝑥, 𝑥 and 𝑚

3. 𝑞 and 𝑝, 𝑛 and 𝑚

4. 360°

5. 𝑎 + 𝑟 < 𝑝 + 𝑥.



1. Place the ruler on the paper and draw two parallel lines (by sliding a set square along the ruler) of

about at least 3 inches apart.

2. Draw any line to intersect the two parallel lines.

3. Label all the angles formed

4. Measure all angles

5. Compare the angles and group together those that are equal. How many groups do you have?

6. From each group, Identify pairs of corresponding angles

7. Are the pairs equal?



In this activity, students will use the concept of measuring to come up with to prove the congruence of

corresponding angles. We students will work in groups of 4. Each group should have a straight edge (a

ruler), a set square a pencil, a plain paper and a protractor.

Answer Keys Day 23:

1.- 2. No response

3.- 4. Responses will differ

5. Responses will differ; 2 groups

6. No response

7. Yes



Use the following diagram to answer questions 1-7.

Given that ∠𝑛 = 63°;

1. Find the value of ∠𝑙 and ∠𝑔.

2. Find the value of ∠𝑚 and ∠𝑓.

3. Find the value of ∠𝑟 and ∠𝑘.

4. Find the value of ∠ℎ.

5. Compare the values of ∠𝑟 and ∠𝑓.

6. List all pairs of corresponding angles.

7. Deduce the property that each pair in 6 has.

ℎ 𝑘

𝑛 𝑟

𝑙 𝑚

𝑔 𝑓



Use the following diagram to answer questions 8-20 if 𝑡 is a complement of 14°.

8. Find the value of ∠𝑡.

9. Determine the Supplement of ∠𝑡.

10. Find the value of angles 𝑠, 𝑙,𝑚 and 𝑛.

11. Find the value of angles ℎ, 𝑘, 𝑝 and 𝑔.

12. Find the value of angles 𝑞, 𝑟, 𝑑 and 𝑤.

13. Find the value of angles 𝑡, 𝑣, 𝑒 and 𝑓.

14. What is a right angle?



15. List all angles less than a right angle.

16. List all angles more than right angle.

17. From the list in 15 above, select pairs that are corresponding angles.

18. Identify any common feature in each pair

19. From the list in 16 above, select pairs that are corresponding angles.

20. Identify any common feature in each pair



Answer keys

Day 23:

1. ∠𝑙 = 117° and ∠𝑔 = 63°.

2. ∠𝑚 = 63° and ∠𝑓 = 117°

3. ∠𝑟 = 117° and ∠𝑘 = 63°

4. ∠ℎ = 63°

5. ∠𝑓 = ∠𝑟 = 117°

6. ℎ and 𝑙, 𝑘 and 𝑚, 𝑔 and 𝑛, and 𝑓 and 𝑟

7. In each pair, the angles are equal

8. 76°

9. 104°

10. 𝑠 = 76°, 𝑙 = 76°,𝑚 = 104° and 𝑛 = 104°.

11. ℎ = 76°, 𝑘 = 76°, 𝑝 = 104° and 𝑔 = 104°

12. 𝑞 = 76°, 𝑟 = 76°, 𝑑 = 104° and 𝑤 = 104°

13. 𝑡 = 76°, 𝑣 = 104°, 𝑒 = 104° and 𝑓 = 76°

14. An angle whose measure is 90°

15. ℎ, 𝑘, 𝑙, 𝑠, 𝑡, 𝑓, 𝑟 and 𝑞

16. 𝑔, 𝑝,𝑚, 𝑛, 𝑒, 𝑣, 𝑑 and 𝑤

17. ℎ and 𝑠, 𝑘 and 𝑙, 𝑠 and 𝑡, 𝑓 and 𝑟, 𝑙 and 𝑓, and 𝑡 and 𝑞, ℎ and 𝑞, and 𝑘 and 𝑟

18. They are equal

19. 𝑔 and 𝑚, 𝑝 and 𝑛, 𝑒 and 𝑤, 𝑣 and 𝑑 , 𝑔 and 𝑤, 𝑑 and 𝑝, 𝑛 and 𝑡, and 𝑚 and 𝑒

20. They are equal.



Find the value of ∠𝑇𝑊𝑆 and ∠𝑊𝑉𝑅 hence compare their values?

𝑃

Q

R

S

T

123°

U

V

W



Answer Keys

Day 23:

∠𝑇𝑊𝑆 = 123°; ∠𝑊𝑉𝑅 =123°

They are all equal



Use the following diagram to answer the following questions

1.The ratio of AP:PC = 1:1. If AP= 2in, what is PC?

2. The ratio of AB:BD = 1:1. If AB= 16 in, what is AD?

3. The ratio of AT:CT = 2:1. If AT= 12in, what is CT?

4. The ratio of AT:CT = 2:1. If AT= 12in, what is AC?

5. G is the midpoint of AF. If AF is 14 in, what is the length of GF?



Answer Keys

Day 24:

1. 2 𝑖𝑛

2. 32 𝑖𝑛

3. 6 𝑖𝑛

4. 6 𝑖𝑛

5. 7 in



1. Cut the four feet string.

2. Make knots at a half feet from each end so that it leaves a 3 feet distance in between the notes.

3. Cut a 5 feet string and tie it to the center of the first string leaving a half feet one side and 4.5 feet on

the other side.

4. Cut a two 5.5 feet strings and tie each at the knots of the first string and also at a common point 4

feet length (from the common knot of the first and second string) on the second string. The diagram is

shown below.

0.5 feet

4.5 feet

0.5 feet

4 feet

0.5 feet

5 feet

5 feet



5. Let four students, each hold each end of the strings as shown.

6. Each student should make sure that the string he/she is holding is slightly tight. Student 4 should

move left right and backward until the 3 strings attached to the first string are tight.

7. Let a fifth student measure the angle (using the protractor) between the two main strings, that is,

students 1 -3 and students 2-4 strings. What is the approximate size of each angle?

8. How may we refer to the students 2 - 4 string in relation to that of students 1-3?

0.5 feet

4 feet

0.5 feet

5 feet

5 feet

Student

1

Student

2

Student

3

Student

4



This is a very interesting activity where students will prove the equality of the points on a perpendicular

bisector to the endpoints of a line using a number of strings. Students will be in groups of at least 7.

Each group is required to have a fairly long string, like 20 feet, blackboard protractor, that is, any

instrument that can measure a right angle.

Answer Keys Day 24:

1. - 6. No response

7. 90°

8. Perpendicular bisector



In the figure below, CE is a perpendicular bisector of AB and CD = 12 in. Use it to answer questions 1 –

10.

1. Find the size of AD if DB is 8 in.

2. Find value of angle 𝐴𝐷𝐶.

3. Find the length of CB.

4. Find the size of AC.

5. Compare the size of AC and CB.

6. If angle 𝐴𝐶𝐵 = 67.38, find the size of angle DCB.

7. Identify if any, a rigid motion relation triangles ADC and DBC.

8. Explain your answer in 7.

9. Identify the existence or non-existence of congruence of triangles ADC and DBC.

10. Explain your answer in 9 above.

D A B

C

E



In the figure below, TU is perpendicular to PR, PS = SR and QS = 6 in. Use it to answer questions 11 – 20.

11. Find the size of PS if SR is 9 in.

12. Find the ratio of PR to PS.

13. Find the length of PQ.

14. Find the size of RQ.

15. Compare the size of PQ and QR.

16. Find the size of angle 𝑄𝑆𝑅 giving reason(s).

17. Identify if any, a rigid motion relation triangles PQS and QRS.

18. Explain your answer in 17.

19. Identify the existence or non-existence of congruence of triangles ADC and DBC.

20. Explain your answer in 19 above.



Answer keys

Day 24:

1. 8 in

2. 90°

3. 14.42 in

4. 14.42 in

5. They are equal

6. 33.69°

7. Reflection

8. Triangle ACB is symmetrical about CD

9. The true triangles are congruent

10. They are related due to a rigid transformation whose existence implies the existence of

congruence

11. 9 in

12. 2 ∶ 1

13. 10.82 𝑖𝑛

14. 10.82 𝑖𝑛

15. They are equal

16. 90° since UQ intersects PR perpendicularly

17. Reflection

18. Triangle PQR is symmetrical about SQ

19. The true triangles are congruent

20. They are related due to a rigid transformation whose existence implies the existence of

congruence



Find the value of ST given that VT is the perpendicular bisector or SU and 𝑉𝑆 = 3 𝑖𝑛, 𝑈𝑇 = 6𝑐𝑚 and the

perimeter of triangle STU is 18 in. Compare ST and UT.

S

U

T V



Answer Keys

Day 24:

𝑆𝑇 = 6𝑐𝑚

They are all equal

138


Geometry

Week 5 Assessment


139

Week 5

Weekly Assessments

140

Week #5

1. Use the figure below to answer the

questions that follow.

a) Find the value ℎ. b) Find the value of 𝑗. c) Find the value of 𝑘.

2. Use the figure below to answer the questions that

follow.

a) Find the value of 𝑎. b) Find the value of 𝑏.



a) By corresponding angle property, what is the value 𝑓? b) By supplementary angles property, what is the value of 𝑐? c) By supplementary angles property, what is the value of 𝑑?

4. Use the figure below to answer the questions that follow. a) Find the value of 𝑒. b) Find the value of 𝑛. c) Find the value of 𝑟. d) Find the value of 𝑞.

𝑓 𝑒 113°

ℎ

𝑖 𝑗 𝑘

𝑙

79° 𝑎 𝑏

𝑐 𝑎 55°

𝑏

𝑓 𝑑

𝑚 𝑒 143°

𝑛

𝑡 𝑟 𝑞

𝑠

141

5. Identify the rigid motion involved in each case. a) b)

6. Use the figure below to answer the questions that follow. a) Find the value of 𝑑. b) Find the value of c. c) Find the value of 𝑎.

𝑐 𝑎

145°

𝑏

𝑑

142

Week 5 - KEYS

Weekly Assessments

143

Week #5 KEY

1. Use the figure below to answer the questions that follow. a) Find the value ℎ. 67° b) Find the value of 𝑗. 67° c) Find the value of 𝑘. 113°

2. Use the figure below to answer the questions that follow. a) Find the value of 𝑏. 101° b) Find the value of 𝑎. 79°



a) By corresponding angle property, what is the value 𝑓? 55° b) By supplementary angles property, what is the value of 𝑐? 125° c) By supplementary angles property, what is the value of 𝑑? 125°

4. Use the figure below to answer the questions that follow. a) Find the value of 𝑒. 37° b) Find the value of 𝑛. 37° c) Find the value of 𝑟. 37° d) Find the value of 𝑞. 143°

𝑓 𝑒 113°

ℎ

𝑖 𝑗 𝑘

𝑙

79° 𝑎 𝑏

𝑐 𝑎 55°

𝑏

𝑓 𝑑

𝑚 𝑒 143°

𝑛

𝑡 𝑟 𝑞

𝑠

144

5. Identify the rigid motion involved in each case. a) Glide reflection b) Translation

6. Use the figure below to answer the questions that follow. a) Find the value of 𝑑. 35° b) Find the value of c. 145° c) Find the value of 𝑎. 145°

𝑐 𝑎

145°

𝑏

𝑑



1. Given that the pair of lines intersected by the transversal is parallel, find the value of the x in the

following figures.

(a)

(b)

(c)

ሺ2𝑥 + 17ሻ°

ሺ3𝑥 − 41ሻ°

ሺ11𝑥ሻ°

ሺ9𝑥 + 18ሻ°

ሺ𝑥 + 5ሻ°

ሺ91 − 𝑥ሻ°



2. In the figure below,MN⃗⃗⃗⃗ ⃗⃗ and PQ⃗⃗⃗⃗ ⃗ intersect at O as shown.

(a) Find the value of r.

(b) Hence, find ∠MOP :

ሺ2𝑟 − 111ሻ°

ሺ𝑟 + 24ሻ°

M

P

N

Q

O



Answer Keys

Day 26:

1. (a) 𝑥 = 58°

(b) 𝑥 = 9°

(c) 𝑥 = 43°

2. (a) 𝑟 = 135°

(b) ∠MOP = 21°



1. Place the carbon paper between the two plain papers provided make sure they are carefully aligned.

2. Draw two intersecting lines (at any angle), PQ⃡⃗ ⃗⃗ and RS⃡⃗⃗⃗ on the top plain paper.

2. Label the intersection point O as shown below.

3. Label the two pairs of vertical angles as shown below.

4. Separate the two papers and on the duplicate, cut out carefully angles α ́ and β ́ using the pair of

scissors provided.

P

Q R

S

O

𝛽

P

Q R

S

O

𝛼 �́�

𝛽ሖ



5. Place the cut out of angle α ́on angle 𝛼 on the original plain paper. What do you notice? What does

this suggest about the two angles?

6. Place the cut out of angle β ́on angle β on the original plain paper. What do you notice? What does

this suggest about the two angles?



In this activity, students will be able to verify that vertical angles are equal in preparation for the lesson.

The students will work in groups of four. Each group will be provided with two A4 size plain papers, an

A4 size carbon paper, a pencil, a ruler, a pair of scissors.

Answer Keys

Day 26:

1. No response

2. No response

3. No response

4. No response

5. The cut outfits exactly on the angle suggesting that the angles are equal.

6. The cut outfits exactly on the angle suggesting that the angles are equal.



Use the figure below to answer questions 1 - 11. PQ⃡⃗ ⃗⃗ and RS⃡⃗⃗⃗ are parallel. AB⃡⃗⃗⃗ ⃗ intersects the two parallel

lines at points K and L. We are given ∠LKQ = 𝛽.

1. Find the measure of ∠LKP in terms of 𝛽.

2. Find the measure of ∠KLS in terms of 𝛽.

3. Compare ∠KLS to ∠LKP. What do you discover about the two angles?

4. Find the measure of ∠KLR in terms of 𝛽.

5. Compare ∠LKQ to ∠KLR. What do you notice about the two angles?

6. Find the measure of ∠AKQ in terms of 𝛽.

7. Find the measure of ∠BLR in terms of 𝛽.

8. Compare ∠AKQ to ∠BLR . What do you conclude?

9. Find the measure of ∠AKP in terms of 𝛽.

10. Find the measure of ∠BLS in terms of 𝛽.

11. Compare ∠AKP to ∠BLS . What do you notice?



Use the figure below to answer questions 12-15. Lines AB and CD intersect to form the angles shown

and ∠DOB = θ.

12. Find the measure of ∠AOD in terms of 𝜃.

13. Find the measure of ∠BOC in terms of 𝜃.

14. Compare ∠AOD to ∠BOC . What do you notice about these two angles?

15. Find the measure of ∠AOC in terms of 𝜃 using the measure of ∠AOD.

16. Compare ∠DOB to ∠AOC . What do you notice about these two angles?

Use the figure below to answer questions 17-20. JK⃡⃗ ⃗ and LM⃡⃗⃗⃗ ⃗ are parallel. PQ⃡⃗ ⃗⃗ intersects the two parallel

lines at points to form the angles shown and ∠KAP = 𝑝°.

17. Find the measure of ∠JAP in terms of 𝑝.

𝜃

A

B

C

D

O



18. Find the measure of ∠BAK in terms of 𝑝.

19. Find the measure of ∠BAJ in terms of 𝑝 using the measure of ∠BAK you have found in question 18

above.

20. Compare ∠BAJ to ∠KAP and write done your conclusion about the measures of the two angles.



Answer keys Day 26:

1. ∠𝐿𝐾𝑃 = 180° − 𝛽

2. ∠𝐾𝐿𝑆 = 180° − 𝛽

3. ∠𝐿𝐾𝑃 = ∠𝐾𝐿𝑆 = 180° − 𝛽; They are equal

4. ∠𝐾𝐿𝑅 = 𝛽

5.∠LKQ = ∠KLR = 𝛽; They are equal

6. ∠𝐴𝐾𝑄 = 180° − 𝛽

7. ∠𝐵𝐿𝑅 = 180° − 𝛽

8. ∠𝐴𝐾𝑄 = ∠𝐵𝐿𝑅 = 180° − 𝛽;They are congruent

9. ∠𝐴𝐾𝑃 = 𝛽

10. ∠𝐵𝐿𝑆 = 𝛽

11.∠AKP = ∠BLS = 𝛽; They are equal

12. 180° − 𝜃

13. 180° − 𝜃

14. They are equal

15. 𝜃

16. They are equal

17. 180° − 𝑝°

18. 180° − 𝑝°

19. 𝑝°

20. They are congruent



In the figure below, KL⃡⃗⃗⃗ and MN⃡⃗⃗⃗⃗⃗ are parallel. PQ⃡⃗ ⃗⃗ intersects the two parallel lines at points A and B. We

are further given ∠BAL = θ.

(a) Find the measure of ∠ABN in terms of 𝜃.

(b) Using the expression for the measure of ∠ABN you have found in part (a) above, find the measure

of ∠ABM in terms of 𝜃.

(c) Compare ∠ABM to ∠BAL. What do you discover about the two angles?

A

K L

M B N

P

Q

𝜃



Answer Keys

Day 26:

(a) ∠ABN = 180° − 𝜃

(b) ∠ABM = θ

(c) ∠ABM = ∠BAL = θ; The two angles are congruent.



1. A straight line AB passes through points K(8,4) and L(4,2).

a) Find the slope of line AB.

b) Find the equation of line AB.

2. A straight line KL passes through points M(5,10) and N(7,6).

a) Find the slope of the line.

b) Find the equation of the line KL.

3. A Straight line AB passes through a point P(2,1). If the same line is subjected to a translation of 3 units

upwards, what will be the new coordinates of point P.



Answer Key

Day 4

1 a) 1

2

b) y=𝑥

2

2 a) −2

b) 𝑦 = −2𝑥 + 20

3. (2,4)



1. Position the set square and the ruler as shown below.

2. Holding the ruler and the set square in the same position, carefully draw a line along the edge AB of

the set square.

3. Holding the ruler in the same initial position, carefully slide the set square along edge CD of the ruler

to another position in the direction shown below.



4. In the same way, holding the ruler and the set square in the same position, carefully draw a line along

the edge EF of the set square.

5. Leaving the ruler unmoved, carefully remove the set square and observe the pair of lines you have

drawn. What kind of lines are they?

6. Compare the steepness of one line with respect to the other. What is your conclusion about the

steepness of this pair of lines?

7. If you another line in the same way along position GH as shown below, what will be its steepness in

comparison with the pair of lines you have drawn previously?

8. What conclusion regarding the type of lines in relation to their steepness do you deduce from the

type of lines you have drawn in this activity?

C

D

G H



In this activity, students will work in groups of four to discover the slope criteria of parallel lines by

drawing three parallel lines and comparing the steepness. The students in the respective groups will

require a pencil, a protractor, a set square and an A4 size plain paper. It is perceived that the students

have discussed the basic properties of parallel lines.

Answer Keys

Day 27:

1. No response

2. No response

3. No response

4. No response

5. Parallel lines

6. They have the same steepness.

7. It will have the same steepness.

8. If two or more lines are parallel, then they have the same steepness



Two parallel lines AB and CD share a perpendicular bisector. Line AB passes through points A(3,4) and

B(5,3). Line CD passes through points C(-2,8) and D(0,7). The perpendicular bisector passes through

points Q(3,3) and R(4,5) Use this information to answer questions 1-6.

1. Find the slope of line AB.

2. What is the slope of line CD?

3. Compare the slope of line AB and that of line CD.

4. What is the slope of their perpendicular bisector?

5. Multiply the slope of line AB with that of the perpendicular bisector. What is their product?

6. Find the product of the slope of line CD and the slope of the perpendicular bisector.

Two lines, 𝐿1 and 𝐿2 are parallel to each other. 𝐿1 passes through points A(6,3) and B(4,6) while

𝐿2 passes through points C(4,7) and D(2,10). Use this information to answer questions 7-9.

7. Find the slope of 𝐿1


9. Compare the slope of 𝐿1 and that of 𝐿2

Two lines 𝐿3 and 𝐿4 are perpendicular to each other. 𝐿3 passes through points E(5,8) and F(3,9) while 𝐿4

passes through points G(1,2) and the origin. Use this information to answer questions 10-12.

10. Find the slope of 𝐿3.

11. Find the slope of 𝐿4.

12. What is the product of the slope of 𝐿4 and that of 𝐿3?



Lines ST and MN are parallel to each other. Line ST passes through points S(2,3) and T(5,9). Line MN Passes

through points M(3,4) and N(6,10). Use this information to answer questions 13 to 15.

13. Find the slope of line ST

14. Find the slope of line MN

15. Compare the slopes of the two lines.

Line PT crosses two lines 𝐿5 and 𝐿6 such that it makes a right angle with them. Line PT passes through

points P(4,7) and T(2,1), 𝐿5 passes through points A(12,9) and B(9,10) and 𝐿6 passes through points G(4,3)

and F(1,4). Use this information to answer questions 16 to 20.

16. Find the slope of line PT


18. Find the product of the slope of line PT and the slope of 𝐿5


20. Find the product of the slope of line QR and the slope of 𝐿6



Answer Keys

Day 27:

1. −1

2

2. −1

2

3. They are equal.

4. 2

5. -1

6. -1

7. −3

2

8. −3

2

9. They are equal.

10. −1

2

11. 2

12. -1

13. 2

14. 2

15. They are equal

16. 3

17. −1

3

18. -1

19. −1

3

20. -1



1. Two lines AB and CD are perpendicular to each other, and they intersect at a point V(3,6). Line CD

passes through a point U(6,15) while line CD passes through a point W(0,7).

a) What is the slope of line AB?

b) Find the slope of line CD

C) Find the product of slope of line AB and the slope of line CD.



Answer Keys

Day 27:

1. a) 3

b) −1

3

c) -1



1. Two lines AB and CD are such that and the former passes through points A(2,3) and B(4,7) while the

latter passes through points C(1,2) and D(4,8).

a) Find the slope of line AB

b) Find the slope of line CD.

2. Two lines DF and DH intersect at point D(3,2). Line DF and DH pass through the point F(5,4) and H(4,3)

respectively.

a) Find the slope of line DF

b)Find the slope of line DH

3. Find the slope of a line that is perpendicular to another whose slope is 3.



Answer Key Day 4

1 a) 2

b) 2

2 a) 1

b) -1

3. −1

3



1. Plot the x y plane with a scale of two bigger squares representing one unit as shown below.

2. Mark points ሺ1, −1ሻ and ሺ−2,1ሻ and label them A and B respectively.



3. Join points A and B with a straight line as shown below.

4. Mark points ሺ−3,−1ሻ and (-1,2) and label C and D respectively.

5. Using a ruler and a pencil join points C and D with a straight line as shown below.

6. Label the point of intersection of lines AB and CD as F.

7. Identify any two points on line AB and use them to find the slope of line AB.

What do you get as the slope of line AB?

8. Identify any two points on line CD and use them to find the slope of line CD.

What do you get as the slope of line CD?

9. Multiply the slope of line CD with the slope of line AB. What is their product?

10. Using a protractor measure ∠𝐴𝐹𝐶. What the size of ∠𝐴𝐹𝐶?



In this activity, students are required to draw two lines in x y-plane, find their slopes and measure the

angle between them. Students are required to work in groups of at least three. Each group is required to

have a ruler, a pencil, a graph paper and a protractor.

Answer Keys

Day 28:

1-6. No response

7. −2

3

8. 3

2

9. −1

10. 90°



Use the following information to answer questions 1 and 2.

Line AB is parallel to CD and passes through the points A(1,2) and B(4,4).If line CD passes through point

Dሺ3,7ሻ;

1. Find the slope of line AB

2. Find the equation of line CD

Use the following information to answer questions 3 - 5.

Two perpendicular lines ST and SV intersect at a point S(3,4). Line ST passes through point T(5,5).

3. Find the slope of line ST.

4. Find the slope of the line SV

5. Find the equation of the line SV

Use this information to answer questions 6 - 7.

A Line defined by 𝑦 = 3𝑥 + 4 is perpendicular to line DF. If the coordinates of D is (2,4)

6. Find the slope of the line DF

7. Find the equation of the line DF

Use the rectangle to answer questions 8 – 13.

DEFG is a rectangle. Two vertices of the rectangle are 𝐷ሺ4,3ሻ and 𝐸ሺ7,1ሻ

8. Find the slope of side DE

9. What is the slope of the side GF?

10. Find the slope of the side EF

11. Find the equation of side EF

12. What is the slope of side DG?



13. If a line is drawn such that it coincides with the side DG, what will be the equation of that line?

Use this information to answer questions 14 - 16

Lines TU and UV intersect perpendicularly at a point 𝑈ሺ−31,9ሻ. If the coordinates of T is ሺ−11,21ሻ.

14. Find the slope of the line TU

15. What is the slope of the line UV?

16. Find the equation of the line UV

Use the following information to answer question 17-19.

Line PR is parallel to line ST and passes through points 𝑃ሺ5,0ሻ and 𝑅ሺ2,9ሻ. Line ST passes through a point

𝑆ሺ2,3ሻ.

17. Find the slope of the line PR

18. What is the slope of the line ST?

19. Find the equation of the line ST.

20. Two perpendicular lines 𝐿1 and 𝐿2 intersect at a point 𝐴ሺ−11,−4ሻ. 𝐿1 passes through a point

𝐵ሺ3,5ሻ. Find the equation of 𝐿2



Answer Keys Day 28:

1. 2

3

2. 𝑦 = 2

3𝑥 + 5

3. 1

2

4. -2

5. 𝑦 = −2𝑥 + 10

6. −1

3

7. 𝑦 = −1

3𝑥 +

14

3

8. −2

3

9. −2

3

10. 3

2

11. 𝑦 = 3

2𝑥 −

19

2

12. 3

2

13. 𝑦 = 3

2𝑥 − 3

14. 4

5

15. −5

4

16. 𝑦 = −5

4𝑥 −

119

4

17. −3

18. −3

19. 𝑦 = −3𝑥 + 9

20. 𝑦 = −14

9𝑥 −

190

9



1. ABCD is a square. Two of its vertices are A(2,4) and B(4,1) as shown below.

Without drawing, find the equation of side BC

B(4,1)

A(2,4) C

D



Answer Keys

Day 28:

1. 𝑦 =3

2𝑥 − 5



1. Find the distance between the following points

(a). ሺ2,4ሻ and ሺ−6,4ሻ.

b).ሺ5,3ሻ, ሺ5, −2ሻ

c). ሺ3,8ሻ, ሺ−1, 2ሻ

2. The ratio of 𝑦 to 𝑝 is 3 ∶ 5. If 𝑝 = 35, find the value of 𝑦.

3. Jastine and Justo are to share 18 pieces of candy in the ratio 1: 2 respectively. How many more pieces

of candies do Justo get more than Jastine?



Answer Key

Day 29

1. a). 8 units

b). 5 units

c). 7.211 units

2. 21

3. 6.



1. Take out the rod, place it on the part and marks its ends on the paper. Label the marks as M1 and M2

respectively.

2. Place one end of the rod at M2 and the other end as a new mark, M3 where M3, M2and M1 must be

on the same straight line.

3. Continue in that manner until you get M6 with M1 to M6 all lying on the same straight line.

4. How marks do you have in total?

5. How many spaces between the marks are there?

6. Identify mark 3, how many marks spaces (of the size of the rod) are before Mark 3.

7. Identify mark 3, how many marks spaces (of the size of the rod) are after Mark 3.

8. Find the ratio between the value in 6 and that of 7 respectively.

9. Let M1, M2, …, M6 be on a line that is on 𝑥- axis where M1 is at the origin. What would be the

coordinates of M1?

10. Identify the coordinates of M1, M3, and M6.



11. Taking P = M3, verify that the formula 𝑥 =𝑚𝑥2+𝑛𝑥1

𝑚+𝑛; 𝑦 =

𝑚𝑦2+𝑛𝑦1

𝑚+𝑛 is true if 𝑃ሺ𝑥, 𝑦ሻ is the

coordinates of M3.



In this activity, we would like to verify the formula for proportional division of a line. Students will work

in groups of 4. Each group will require a plain paper, a standard measurement tool which is a small grass

rod (or small rod that can serve the purpose) of 2 into 3 in, pencil.

Answer Keys

Day 29:

1 – 3.No response

4. 6

5. 5

6. 2

7. 3

8. 2 ∶ 3

9. ሺ0,0ሻ

10. 𝑀1ሺ0,0ሻ, 𝑀3ሺ2,0ሻ, 𝑀6ሺ5,0ሻ

11.𝑃ሺ2,0ሻ; 𝑥 = 2, 𝑦 = 0, 𝑚: 𝑛 = 2: 3, 𝑥1 = 𝑦1 = 𝑦2 = 0; 𝑥2 = 5

𝑥 =𝑚𝑥2+𝑛𝑥1

𝑚+𝑛=

2ሺ5ሻ+3ሺ0ሻ

2+3= 2 𝑦 =

𝑚𝑦2+𝑛𝑦1

𝑚+𝑛=

2ሺ0ሻ+3ሺ0ሻ

3+2= 0




Given the following endpoints of a line segment, 𝐴ሺ−3,−2ሻ and 𝐵ሺ6,−5ሻ, find the coordinates of the

point that devides the line in the following ratios.

1. 1 ∶ 2

2. 2 ∶ 1

3. 1 ∶ 1


Given the following endpoints of a line segment, 𝐶ሺ−8,−7ሻ and 𝐷ሺ8,1ሻ, find the coordinates of the

point that devides the line in the following ratios.

4. 1: 7

5. 1 ∶ 1

6. 5 ∶ 3

7. 3 ∶ 5

8. 1 ∶ 3

9. 2 ∶ 3



Use the following information to answer questions 10 - 18

The following endpoints of a line segment are 𝑀ሺ−2,4ሻ and 𝑁. Point 𝑇ሺ4,−2ሻ divides the line in the

ratio 1: 1.

10. Find the coordinates of 𝑁.

11. Find the coordinates of a point that divides the line in the ratio 1 ∶ 5.








Use the following information to answer questions 19 - 20

The following endpoints of a line segment are 𝑃ሺ−7,−5ሻ and 𝑄. Point 𝑆ሺ−3,1ሻ divides the line in the

ratio 2: 1.

19. Find the coordinates of a point Q.

20. If Q divides line PR in the ratio 3 ∶ 1, find the coordinates of a point R.



Answer Keys

Day 29:

1. ሺ0, −3ሻ

2. ሺ3, −4ሻ

3. ሺ1.5, −3.5ሻ

4. ሺ−6,−6ሻ

5. ሺ0, −3ሻ 6. ሺ2, −2ሻ

7. ሺ−2,−4ሻ

8. ሺ−4,−5ሻ

9. ሺ4, −1ሻ

10. ሺ10,−8ሻ

11. ሺ0,2ሻ

12. ሺ1,1ሻ

13. ሺ2,0ሻ

14. ሺ6, −4ሻ

15. ሺ7, −5ሻ

16. ሺ8, −6ሻ

17. ሺ3, −1ሻ

18. ሺ9, −7ሻ

19. ሺ−1,4ሻ

20. ሺ1,7ሻ



Find the coordinate of a point C dividing the line segment joining ሺ−1, −3ሻ and ሺ2,4ሻ in the ratio 1.2.



Answer Keys

Day 27:

ሺ0, −1ሻ

187


Geometry

Week 6 Assessment


188

Week 6

Weekly Assessments

189

Week #6 1. Use the graph below to answer the questions that follow.

Find the slope of line AB. b) Find the slope of line CD. c) Calculate slope of AB × slope of CD.

-3 -2 -1 0 1 2 3 4 𝒙

𝒚

𝟏

𝟐

𝟒

𝟑

−𝟏

−𝟐

−𝟑

𝑨

𝑩

𝑪

𝑫

190

2. Use the graph below to answer the questions that follow.

a) Find the slope of EF. b) Find the slope of GF.

-3 -2 -1 0 1 2 3 4 𝒙

𝒚

𝟏

𝟐

𝟒

𝟑

−𝟏

−𝟐

−𝟑

𝑭

𝑮

𝑬

𝑯

191

3. Use the diagram below to answer the questions

that follow.

a) Find the value of 𝑏.

b) Find the value of c.

4. Use the figure below to answer the questions

that follow.

a) Using the properties of angles on a straight line, find the value of 𝑘. b) Using the properties of angles on a straight line find the value of 𝑙.

5. Lines ST and UV are parallel. The equation of ST

is 2𝑦 = 3𝑥 − 4. Line UV passes through

point 𝑉ሺ7, −3ሻ.

a) Find the slope of line UV. b) Find the equation line UV.

6. Find the missing complementary angle.

a) 41° b) 89°

37° 𝑘

𝑙 𝑐 𝑎 𝑏

𝑑 25°

192

Week 6 - KEYS

Weekly Assessments

193

Week #6 KEY 1. Use the graph below to answer the questions that follow.

Find the slow of line AB. −1 b) Find the slop of line CD. 1 c) Calculate slope of AB × slope of CD. 1

-3 -2 -1 0 1 2 3 4 𝒙

𝒚

𝟏

𝟐

𝟒

𝟑

−𝟏

−𝟐

−𝟑

𝑨

𝑩

𝑪

𝑫

194

2. Use the graph below to answer the questions that follow.

a) Find the slope of EF.

−3

2

b) Find the slope of GF.

−3

2

-3 -2 -1 0 1 2 3 4 𝒙

𝒚

𝟏

𝟐

𝟒

𝟑

−𝟏

−𝟐

−𝟑

𝑭

𝑮

𝑬

𝑯

195

3. Use the diagram below to answer the questions

that follow.

a) Find the value of 𝑏.

25°

b) Find the value of 𝑐.

25°

4. Use the figure below to answer the questions

that follow.

a) Using the properties of angles on a straight line, find the value of 𝑘. 143° b) Using the properties of angles on a straight line find the value of 𝑙. 37°

5. Lines ST and UV are parallel. The equation of ST

is 2𝑦 = 3𝑥 − 4. Line UV passes through

point 𝑉ሺ7, −3ሻ.

a) Find the slope of line UV.

3

2

b) Find the equation line UV. 2𝑦 = 3𝑥 − 27

6. Find the missing complementary angle.

a) 41° 39° b) 89° 1°

37° 𝑘

𝑙 𝑐 𝑎

𝑏

𝑑 25°

Unit 2 Test Name ____________________________________


Questions:

1. In the figure below, identify all right angles.

2. Name the angle represented below in four different ways.

3. Find the complements of the following angles:

a) 6°

b) 77°

c) 45°

4. Find the supplements of the following angles:

a) 1°

b) 145°

c) 32°

A

B

C

D

E

O

∅

A

B C

Unit 2 Test Name ____________________________________


5. In a given pair of supplementary angles, the size of the larger angle is four times the size of the

smaller angle. Find the size of the two angles.

6. What is the value of c?

7. Find the value of g!

8. What is the value of a?

40 𝑐

80

g

𝑎 + 10°

45 70

Unit 2 Test Name ____________________________________


9. Define transversal line!

10. Find the value of x!

11. If x and y are two complementary angles and the value of x is 11°, what is the value of y?

12. Find the measure of < 𝐹𝑂𝐷!

70°

𝑥

Unit 2 Test Name ____________________________________


13. Find the value of y!

Unit 2 Test Name ____________________________________


14. Define interior angles!

15. Find the sum of angles a, n, q and r.

16. C is the midpoint of AB. If AB is 22 in what is the length of CB?

Unit 2 Test Name ____________________________________


17. If CE is a perpendicular bisector of AB and if DB is 10 cm, find the size of AD.

18. A straight line JK passes through points A(16,8) and B(8,4). Find the slope of line JK.

19. Find the slope of a line that is perpendicular to another whose slope is 7.

20. Find the distance between (1, -1) and (-7, 5).

Unit 2 Test Name ____________________________________


Answers:

1. ∠AOC, ∠COE

2. ∠B, ∠ABC, ∠CBA, ∠x

3.

a) 84°

b) 13°

c) 45°

4.

a) 179°

b) 35°

c) 148°

5. 144°and 36°

6. 𝑐 = 50°

7. 𝑔 = 280°

8. 𝑎 = 55°

9. Transversal line is a line that crosses two or more parallel lines at different points.

10. 𝑥 = 110°

11. y=79°

12. < 𝐹𝑂𝐷 = 89°

13. y=5

14. Interior angles are angles formed between a pair of parallel lines when a transversal line intersects

the pair of parallel lines.

15. 360°

16. CB = 11 in

17. AD = 10 cm

18. 𝑚 =1

2

19. 𝑚 = −1

7

20. 10 units

Documents

Geometry Complete Unit 2 - High School Math Teachers€¦ · Unit 2 Lesson Plans Name _____ HighSchoolMathTeachers.com©2020 Page 6 Unit: Unit 2 Angles and Lines Course: Geometry