PARALLEL LINES AND TRANSVERSALs 3 for...PARALLEL LINES AND TRANSVERSALs In this investigation you need a protractor and a ruler (or other straight edge). Lay your ruler in the space

Name: ____________________________ Period: ________ 3.1 Parallel Lines and Transversals

PARALLEL LINES AND TRANSVERSALs In this investigation you need a protractor and a ruler (or other straight edge).

Lay your ruler in the space below. Trace along both sides of the ruler so you will have a set of parallel lines.

Then draw a third line that crosses the two parallel lines, this is the transversal. Do not make right angles.

Label all 8 angles starting with 1, 2, 3 and so on. Measure each angle and record its degree measurement in the table.

Angle 1 2 3 4 5 6 7 8

Measurement

Observe which angle pairs are congruent. Choose a color pencil/crayon and color each set of angles which are congruent

the same color. How many colors did you use?

What do you observe about the pairs of angles that are colored differently?

Questions 1-6: Label each angle pair by their relationship “vertical, alternate interior, alternate exterior,

corresponding.” Solve for x, show your work.

Question 7 – 10

Name: _________________________________ Period: ________ 3-2 Rigid Motion and Proving lines ||

Describe a series of rigid motions that maps one figure to the other. Be specific. Do not just say “reflect”

unless you indicate what it is reflected around, or “rotate” unless you say what you are rotating around

and describe the rotation, or “translate” unless you specify how far/in what direction.

1) ∠1 and ∠4 2) ∠2 and ∠6

3) ∠3 and ∠6 4) ∠1 and ∠7

5) ∠8 and ∠2 6) ∠5 and ∠7

Decide whether each statement is TRUE or FALSE. If the statement is false, correct the statement.

7) _____ m || n line m

8) _____ ∠1 and ∠5 are vertical angles

9) _____ ∠2 and ∠8 alternate exterior

10) _____ ∠3 and ∠5 are same side interior line n

For the given information, tell which pair of the lines (if any) above must be parallel. State the

relationship that supports your answer.

Which lines? Support?

Example: ∠1 ≅ ∠9 line m || n If alternate exterior angles are ≅ then lines ||

11) ∠1 ≅ ∠5

12) ∠10 + ∠11 = 180ᵒ

13) ∠10 ≅ ∠4

14) ∠12 ≅ ∠4

15) ∠12 + ∠7 = 180ᵒ

16) ∠1 ≅ ∠9

Name: _________________________ Period: ________ 3.3 Sidewalk Lab

Part 1.

Your group has been asked to determine the quality of the layout of the concrete sections of sidewalk

poured at Tanque Verde High School. The breaks in the concrete should be parallel lines. Your group

should prove those sections are indeed parallel.

1) With your group, find a section of sidewalk that contains at least three adjacent rectangular sections.

2) Using appropriate tools, draw a CHALK transversal through all three sections. Record on diagram.

3) Measure at least three angles. Record on diagram below.

4) Measure the outside edge of all six lengths of the sidewalk. Record on diagram

Measure this width Measure this width Measure this width

Check list:

□ These three rectangles represent

sections of sidewalk

□ Draw your transversal (chalk line)

□ Label the diagram with your

angle measurements

□ Label your 6 segment widths

Measure this width Measure this width Measure this width Measure this width Measure this width Measure this width

5) Classify an angle pair that your group measured _______________________________________

What relationship do those angles have that proves that the line segments are parallel? You should write a

conditional statement that starts with “If ------- are ----- then lines are parallel”

6) How are the outside widths of the cement blocks related? How do those measurements prove that the

line segments are parallel?

Part 2 A sidewalk…

2 ∠1

3 4

5

7

6

∠ 8

1) If the sidewalk cracks, are parallel, list the 4 angles that are congruent to ∠5.

2) What kind of angle pair are ∠1 and ∠8?

3) How would those angles be related if the segments in the sidewalk are parallel?

4) If the line segments are parallel and ∠2 = (5x – 3)o and ∠5 = 4(x+2)o what does ∠6 measure?

5) If the segments that are the sidewalk cracks are parallel, and the m∠1 is twice the measure of ∠2, find

the measures of each angle in degrees:

m∠1 = _____ m∠2 = _____ m∠3 = _____ m∠4 = _____

m∠5 = _____ m∠6= _______ m∠7 = _____ m∠8 = _____

Name: _________________________ Period: ________ 3.4 Angle Puzzles

1) Find all the angle measurements, show your calculations:

a = _____

b= _____

c= _____

d= _____

e= _____

f= _____

2) What is wrong with each diagram? Explain.

a) 𝐴𝐵 ⃡ ⊥ 𝐶𝐷 ⃡ B c) F M

370 L

C 390

460 E G

420 D H

A

𝐹𝐻 ⃡ 𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑠 𝐺𝑀 ⃡ 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐿

b) 1200

600

>>

>>

1200

3)

4) How many angles must you be given to find all the other angle measurements? Which one(s)?

a= _____

b= _____

c= _____

d= _____

e= _____

f= _____

g= _____

h= _____

k= _____

m= _____

n= _____

p= _____

q= _____

r= _____

s= _____

Name: _________________________ Period: ________ 3.5 Transversals and Angle Pairs

For each diagram of the DOTTED angles, circle ALL the names or properties this pair is GUARANTEED to have

or circle NONE if that’s the case. 1. vertical angles linear pair adjacent angles none alternate interior alt. exterior same-side int. corresponding congruent supplementary complementary

2. vertical angles linear pair adjacent angles none alternate interior alt. exterior same-side int. corresponding congruent supplementary complementary















All of Ms. Jones’ children were born in June. Their birthdays are June 1, June 7, June 12, June 20 and June 29. There are three girls named Mary, Elvira and Joan and there are two boys named Douglas and Timothy. Ms. Jones bought these five presents for them: a book, a coat, concert tickets, a dress, and an electronic game. From the information given, determine the birthday and present received by each child. 1) Timothy’s birthday comes before that of the girl who received a dress but after the girl who received a coat. 2) Douglas’s birthday comes before Elvira’s birthday but after the birthday of the girl who received an electronic game. 3) Elvira did not receive the dress and neither did Joan 4) Douglas did not get the book as a present.

Birthday Gift

Douglas

Elvira

Joan

Mary

Timothy

Name: __________________________________ Period______ 3.6 Review for Quiz: Parallel Lines,

Transversals and Parallelism

1) Lines m || n || p. Use the figure to identify the type of angle pairs indicated.

a) ______________________________ b) ______________________________

c) ______________________________ d) ______________________________

2) Find the indicated angle measures

__________________________ __________________________ _________________________

3) Solve for x 4) Find the value of x, y and z.

1& 5 2& 8

3& 5 3& 6

5. Describe a series of rigid motions (or just 1 if you’re

clever) that would map ∠10 onto ∠3. Feel free to label the

diagram with labels and extra names that help you be more

precise in your explanation.

6. Determine which lines (if any) are parallel, using the supplied information. State the reason why the lines must be

parallel, if they are. If there is no guarantee that lines are parallel, say there isn’t enough information. Assume that any

previous results of parallelism do not affect subsequent questions.

7.

111 o line m In order for line m || line p what is the value of x?

(2x+9)o line p

What kind of angle pair are the two angles in the diagram?

8. Each parking space is measured at 90o. What is the number of the parking space under the car?

Which Lines are parallel? Reason:

∠2 ≅ ∠10 m || n If alternate interior angles are congruent then lines are parallel.

∠6 ≅ ∠8

∠1 ≅ ∠5

∠6 ≅ ∠7

∠8 + ∠9 = 180°

∠6 ≅ ∠12

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PARALLEL LINES AND TRANSVERSALs 3 for...PARALLEL LINES AND TRANSVERSALs In this investigation you need a protractor and a ruler (or other straight edge). Lay your ruler in the space