Geometry Support Packet Unit 1 - Mater Academy Charter

rs

Geometry Support Packet

4-

Cuovui

UNIT #1

Proofs, Parallel and

Perpendicular Lines

Lesson 1.4 • Polygons

Name Period

For Exercises 1-8, complete the table.

Polygon name Number of sides Number of diagonals

1. Triangle

2. 2

3. 5

4. Hexagon

S. Heptagon

6. 8

7. 35

8. 12

Date

For Exercises 9 and 10. sketch and label each figure. Mark the congruences.

9. Concave pentagon PENTA, with external 10. Equilateral quadrUateral QUAD, withdiagonal BT, and TA = PE. LU.

For Exercises 11-14, sketch and use hexagon ABCDEF.

11. Name the diagonals from A.

12. Name a pair of consecutive sides.

13. Name a pair of consecutive angles.

14. Name a pair of non-intersecting diagonals.

For Exercises 15-18, use the figures at right.

MNOPQ s RSTUV

15. m^N=

16. VR =

17. m/LP =

18. 0N=

16.1

7.2

M

U

19. The perimeter of a regular pentagon is 31 cm. Find the length ofeach side.

CHAPTER 1 Discovering Geometry Practice YourSkills

82008 Key Curriculum Press

Lesson 1.5 • Triangles

Name Period

For Exercises 1-5, use the figure at right. Name a pair of

1. Parallel segments

2. Perpendicular segments

3. Congruent segments

4. Supplementary angles

5. Linear angles

For Exercises 6 and 7, sketch, label, and mark each figure.

6. Isosceles obtuse triangle TRI with vertex angle T.

• »

C D E F

\ / /\

7. Scalene right triangle SCA with midpoints L, M, and N on SC, CA,and SA, respectively.

Date

For Exercises 8 and 9, use your geometry tools to draw each figure.

8. Acute isosceles triangle ACD withvertex 9. Scalene right triangle RGH.angle A measuring 40®.

For Exercises 10-12, use the graph at right.

10. Locate F so that AABFis a right triangle.

11. Locate D so that AABD is an isosceles triangle.

12. Locate Gso that AABC is scalene and not a right triangle. A (0,0)

-T

• C{8.3)

B(8.0)

Discovering Geometry Practice YourSkills

C2008 Key Curriculum PressCHAPTER 1

Lesson 1.3 *What's a Widget?

Name Period

For Exercises 1-9, match each term with one of the items (a to i) below.

a.

90°J— f

b.

e.

Date

1. Vertical angles 2. Obtuse angle

3. Right angle 4. Complementary angles

5. Congruent angles 6. Linear pair of angles

7. Bisected angle 8. Perpendicular lines

9. Congruent segments

10. If mZ^P - 13°, mA.Q = 77°, and Z.Q and /LR are complementary, whatcan you conclude about Z.Pand Explain your reasoning.

For Exercises 11-13, sketch, label, and mark a figure showingeach property.

11. II €2, €2 -L €3 12. PQ 1 PR 13. /LBAC= LXAY, CX= BC

Discovering Geometry Practice Your Skills

C2008 Key Curriculum PressCHAPTER 1

Lesson 2.2 • Finding the nth Term

Name Period Date

For Exercises 1-4, tell whether the rule is a linear function.

1.n 1 2 3 4 5

2.n 1 2 3 4 5

f\n) 8 15 22 29 36 gin) 14 11 8 5 2

3.n 1 2 3 4 5

4.n 1 2 3 4 5

h[n) -9 -6 -2 3 9 m 3

2 -I2

02

For Exercises 5 and 6, complete each table.

b.n 1 2 3 4 5

6.tt 1 2 3 4 5

f[n) = 7n - 12 gin) = -8m - 2

For Exercises 7-9, find the function rule for each sequence. Then find the50th term in the sequence.

7.50

f[n) 13 17 21 25 29

8.50

^(n) 1 -4 -9 -14 -19

9.I 50

h(n) 6.5 7.5 8 8.5

10. Use the figures to complete the table.

n 1 2 3 4 5 n ... 50

Numberof triangles 1 5 9

11. Use the figures above to complete the table. Assume that the area of thefirst figure is 1 square unit.

n 2 3 4 5 « 50

Area offigure 1 4 16

Discovering Geometry Practitx Your SkillsC2008 Key Curriculum Press

CHAPTER 2 11

Lesson 2.3 • Mathematical Modeling

Name Period

1. Draw the next figure in this pattern.

a. How many small squares will there be in the10th figure?

b. How many in the 25th figure?

c. What is the general function rule for this pattern?

Date

H

2. If you toss a coin, you will get a head or a tail. Copy andcomplete the geometric model to show all possible results ofthree consecutive tosses.

a. How many sequences of results are possible?

b. How many sequences have exactly one tail?

c. Assuming a head or a tail is equally likely, what is theprobability of getting exactly one tail in three tosses?

<

3. If there are 12 people sitting at a round table, how many different pairsof people can have conversations during dinner, assuming they canall talk to each other? What geometric figure can you use to modelthis situation?

4. Tournament games and results are often displayed using a geometricmodel. Two examples are shown below. Sketch a geometric model fora tournament involving 5 teams and a tournament involving 6 teams.Each team must have the same chance to win. Try to have as fewgames as possible in each tournament. Show the total numberof games in each tournament. Name the teams a, b, c ... and numberthe games 1, 2, 3 ....

3 teams, 3 games(round robin)

>

>4 teams, 3 games

(single elimination)

H

<HHH

•HHT

12 CHAPTER 2 Discovering Geomefjy Practice Yovr Skills

€2008 Key Curriculum Press

o

Lesson 2.4 • Deductive Reasoning

Name Period

1. AABC is equilateral. Is AABD equilateral? Explain your answer.What type of reasoning, inductive or deductive, do you use whensolving this problem?

2. /LA and Z.D are complementary. Z.A and /.E are supplementary.What can you conclude about Z.D and /LEI Explain your answer.What type of reasoning, inductive or deductive, do you use whensolving this problem?

3. Which figures in the last group are whatnots? What type of reasoning,inductive or deductive, do you use when solving this problem?

/• •V

•> ❖a.

d.

Date

X J

¥T

r1

s

Whatnots Not whatnots Which are whatnots?

4. Solve each equation for x Give a reason for each step in the process.What type of reasoning, inductive or deductive, do you use whensolving these problems?

a. 4x + 3(2 - *) = 8 - Ix. 19 - 2(3x- I)b. ^ = * + 2

5. A sequence begins -4, 1, 6, 11 ...

a. Give the next two terms in the sequence. What type of reasoning,inductive or deductive, do you use when solving this problem?

b. Find a rule that generates the sequence. Then give the 50th term inthe sequence. What type of reasoning, inductive or deductive, doyou use when solving this problem?

DiKOveting Geometry Practice YourSkills02008 Key Curriculum Press

CHAPTEB2 13

Contrapositive:

Irui

Jl

Name Date Period_

77n.f^M Homework 2-1 Conditional Statements

Underline the hypothesis, and circle the conclusion ofeach conditional statement.

1. If you eat breakfast, then you will feel better at school.

2. If two lines are perpendicular, then they form right angles.

3. If two angles are supplementary, then their sum is 180°.

4. If a nonzero number has exactly two factors, then the number is prime.

Write each statement in if-thenform.

5. All students at Hermitage take an English class.

6. All right angles measure 90°.

7. Every dog has four legs.

8. All vertical angles are congruent.

9. All cats chase mice.

Write the converse, inverse, and contrapositive ofeach conditional statement.

10. If it is Saturday, then school is closed.

Converse:

Inverse:

Name Date Perlod_

Homework 2-1 Conditional Statements

11. If two angles are complementary, then they total 90°

Converse:

Inverse:

ContraposUive:_

12. If a line bisects a segment, then the segment is divided into two congruent parts.

Converse:

Inverse:

Contrapositive:.

13. If it rains, then I will not go.

Converse:

Inverse:

Contrapositive:,

14. If two angles form a linear pair, then they are supplementary.

Converse:

Inverse:

Contrapositive:

rw

%

IGName Date Period

rr ri7ri.iiii Homework 2-1 Conditional Statements

Let p represent ''Daniel is angry", and let q represent "Daniel is not havingfun".

Translate thefollowing into symbolicform.

15. Daniel is not angry.

16. Daniel is angry and Daniel is not having fun.

17. Daniel is not angry or Daniel is not having fun.

Translate thefollowingfrom symbolicform to writtenform.

18. pA~q

19. -~qvp

Write the converse ofeach ofthefollowing conditional statements, and then write thebiconditional.

20. If two angles are adjacent, then they share a common ray.

converse:

biconditional:

21. If M is the midpoint of AB, then M is between A and B and AM = MB.

converse:

biconditional:

Name Class Date

Extra Practice (continued)

Chapter 2

If the given statement is not in if-then form, rewrite it Write the converse,inverse, and contrapositive of each conditional statement. Determine the truthvalue of cach statement.

17. irSjT - 7 = 20, thenx = 9. 18. Baseball players are athletes.

19. 'riie product of two even numbers is even.

For cach of the statements, write the conditional form and

then the converse of the conditional. If the converse is true,

combine the statements as a biconditional.

20. The number one is the smallest positive square.

r\ 21. Rectangles have four sides.

22. A squarewitharea 100m^ has sides thatmeasure 10m,

23. Two numbers that add up to be less than 12 have a product less than 37.

24. Three points on the same line are collinear.

Is cach statement a good definition? If not, find a counterexample.

25. A real number is an even number if its last digit is 0,2,4, 6, or 8.

26. A circle with center O and radius r is defined by the set ofpoinls in a plane a

distance r from the point O.

27. A plane is defined by two lines.

28. Segments with the same length are congruent.

r\Prentice HafI Geometry • Extra Practice

Copyngnt © by Pearson Education, Inc., or its affiliates. AllRights Reserved.

5

10

Name Class Dale.


Chapter 2

For RxcrcLscs 29 and 30, write the two statements that form cach biconditional.

Tell whether each statement is true orfalse.

29.1.incs m and n are skew if and only if lines m and « do not intersect.

30. A person can be president of" the United Slates if and only if the person is a citizen

of the United States.

Lesson 2-4

Using the statements below, apply the Law of Detachment or the Law ofSyllogism (o draw a conclusion.

31. IfJorge can't raise money, he can't buy a new car. Jorge can't raise money.

32. IfShauna is early for her meeting, she will gain a promotion. IfShauna wakes upearly, she will be early for her meeting. Shauna wakes up early.

33. iri.inda's band wias the conlesl, they will win S500. IfLinda pracliccs, her bandwill win ihe contest. Linda practices.

rs 34. IfBrendan learns the audition song, he will be selected for the chorus.If Brendan stays after school to practice, he will learn the auditionsong. Brendan stays after school to practice.

For Excrci.scs 35-38, apply the Law ofDetachment, the Law of Syllogism,or both to draw a conclusion. Tell which law(s) you u.scd.

35. If you enjoy all foods, then you like cheese sandwiches. Ifyou like cheesesandwiches, then you eat bread.

36. Ifyou go to a monster movie, then you will have a nightmare. You go to amonster movie.

37. If Catherine is exceeding the speed limii, then she will get a speeding ticketCatherine is driving at 80 mi/h. If Catherine is driving at 80 mi/h, then she isexceeding the speed limh.

38. If Carlos has more than $250, then he can afford tlicvideo game he want-s.If Carlos worked more than 20 hours last week, then he has more than$250. If Carlos works 15 hours this week, then he worked more than 20hours last week.

Prentice Hall Geometry * Extra PracticeCopyright& by Posrson Education, inc., or its afTrfialcs. All Rl9hts RoservGd.

6

11

Lesson 2.5 • Angle Relationships

Name Period

For Exercises 1-6, find each lettered angle measure without usinga protractor.

32°5. f

7/̂70°d/e

For Exercises 7-10, teU whether each statement is always (A),sometimes (S), or never (N) true.

7.

8.

9.

10.

The sum of the measures of two acute angles equals themeasure of an obtuse angle.

If LXAY and LPAQ are vertical angles, then either X, A, and Por X, A, and Q are coUinear.

If two angles form a linear pair, then they are complementary.

If a statement is true, then its converse is true.

For Exercises 11-15, fill in each blank to make a true statement.

11. If one angle of a linear pair is obtuse, then the other is

Date

12. If /LA = Z.B and the supplement of Z.B has measure 22°, thenm/.A =

13. If /.P is a right angle and Z.P and Z.Q form a linear pair, thenmZ-Q is .

14. If Z.S and Z,Tare complementary and Z.T and Z-C7 are supplementary,then /LUis a(n) angle.

15. Switching the "if" and "then" parts of a statement changes thestatement to its

14 CHAPTER 2 Discovering Geometry Praaice Your Skills£2008 Key Curriculum Press

Name .Class Date.

Extra Practice

Chapter 2

Lesson 2-1

Find the next two terms in cach scqucncc.

1. 12, 17, 22,27,32,...

3. 5000, 1000,200,40,...

5.3,0.3,0.03,0.003,...

Draw the next f^re in each sequence.

Z7

2. 1, 1.1,1.11, 1.111,1.1111,.

4. I, 12, 123,1234,...

6.1,4,9,16,25,...

9.1'or a scicncc cxperimenl, you mctusure the height ofaplant every two days. Using inductive reasoning andthe data table at the right, prcdict the height ofihe plant on day 10 of the experiment.

Find one cuuntcrexample to .show that each

conjccture Is false.

10. The result ofa number multiplied by a positive integeris always larger than the original number.

11. A four-sided figurewith four right angles is a square.

12. February has cxactiy 28 days every year.

Lessons 2-2 and 2-3

For Excrciscs 13-15, identify the hypothesis and conclusion of eachconditional.

13. Ifyou can prcdict the future, then you can control the future.

14. If Dan is nearsighted, then Dan nccd.s glasses.

15. If lines/rand m are skew, then lines Aand m arenot perpendicular.

16. Write the converse ofeach statement in Hxereises 13-15.

Plant Height

Day Height (cm)

2 2

4 3.5

6 5

8 6.5

,

Prentice Hall Geometry • Extra PracticeCopyright® by Poarson Education, Inc., or its affiliates. AllRights Roserved.

13

rs

Name

Extra Practice (conlinued)

Chapter 2

Lesson 2-5

39. Algebra You are given lhat 2c^ =2bc +^ withe / 0. Show lhat464c - a by filling in the blanks.

.Class,

ac

a. Given

b. ? and ?

. Date.

a. 2c^=2bc +̂

b. 4c^ = Abe + ac

c. 4c = 46 + a

d._L

e. 46 = 4c - a

c. _2_andDistributive Property

d. Subtraction Property

e.

40. Algebra Solve for x. Show your work. Justify eachstep.

Given: PP hisccisZEPG.

Name the property ofequality or congruence thai justifies going

from the first statement to (he second statement.

{6*-lor

41. ZA/ = ZiV 42. 3x = 24

x = S

43. PQ=RS and RSsTU

Lesson 2-6

Find the value ofx

W-WX (2*+10»

45.

j:

47. Given; Z1 and Z2 are complcmcnlary.

Z3 and Z4 arc complementary.

Prove: Z5 > Z6

PQ^TU

2x'\ 5*+5)

48. Prove or disprove the following statement.

If Z.APB and ZCPD are vortical angles, ZAPS and Z.APE arceomplcmenlary, and ZCPD and ZCPF are complementary, then ZAPEand ZCPF arc vertical angles.

Prentice Hall Geometry • Extra PracticeCopyrigtit© by Poareon Education, Inc., orita affliatos. All Rights Rosorvod.

Lesson 1.1 • Building Blocks of Geometry

Name Period

For Exercises 1-7, complete each statement. PS ~ 3 cm.

1. The midpoint of PQ is

2. JVQ =

3. Another name for NS is

4. S is the

5. P is the midpoint of.

6. NS s

7. Another name for SN is

of SQ.

8. Name all pairs of congruent segments in KLMN. Use thecongruence symbol to write your answer.

N

9. M(—4, 8) is the midpoint of DE. D has coordinates (6, 1). Find thecoordinates of E.

For Exercises 10 and 11, use a ruler to draw each figure. Label thefigure and mark the congruent parts.

Date

N

K<0

cm

M

10. AB and CD with M as the midpointof both AB and CD. AB = 6.4 cm

and CD = 4.0 cm. A, B, and C arenot coUinear.

11. aS and CD. Cis the midpoint of AB, withAC = 1.5 cm. D, not on AB, is themidpoint of AE, with AD —2BC.

12. Sketch six points A, 8. C, D, E, and F, nothree of which are coUinear. Name the linesdefined by these points. How many linesare there?



13. In the figure below, {B, C, H, E) is a set offour coplanar points. Name two other setsof four coplanar points. How many sets offour coplanar points are there?

Cube

CHAPTtR 1

t6

Lesson 1.2 • Poolroom Math

Name

For Exercises 1-5, use the figure at right to completeeach statement.

1. A is the

2. AD is the

3. AD is a

of ^BAE.

_of A BAE

of ADAE.

4. If m/.BAC = 42°, then m^CAE =

5. ADAB s

For Exercises 6-9, use your protractor to find the measure ofeach angle to the nearest degree.

p6. mZ.PRO

8. mZ.O

7. m/.ORT

9. mZ.RTO

Period

For Exercises 10-12, use your protractor to draw and then labeleach angle with the given measure.

10. m/LMNO= 15° U,m/LRIG = 90°

For Exercises 13-15, find the measure of the angle formed by thehands at each time.

13. 3:00 14. 4:00

Date

12. 160°

IS. 3:30

For Exercises 16 and 17, mark each figure with all the given information.

16. mLADB = 90°, AD = BD, ADAB s Z.DBA

B

17. m/.RPQ = 90°, QR = TZ. RT = QZ,AQs AT

CHAPTER 1 Discovering Geometry Practice Your Skills


\(o

r\

Lesson 9.5 • Distance in Coordinate Geometry

Name Period Date

In Exercises 1-3, find the distance between each pair of points.

1. (-5, -5), (1, 3) 2. {-II, -5). (5, 7) 3. (8, -2), (-7, 6)

In Exercises 4 and 5, use the distance formula and the slope of segments toidentify the type of quadrilateral. Explain your reasoning.

4. A{-2, I), B(3. -2). C(8, 1), D(3, 4) 5. 7T:-3, -3), (7(4. 4). V{0, 6), W(-5, 1)

For Exercises 6 and 7, use A/lBCwith coordinates A(4, 14), B(IO, 6), andC(I6, 14).

6. Determine whether AABC is scalene, isosceles, or equilateral. Find theperimeter of the triangle.

7. Find the midpoints M and N of AB and AC, respectively. Find theslopes and lengths of MN and BC. How do the slopes compare? Howdo the lengths compare?

8. Find the equation of the circle with center (—1, 5) and radius 2.

9. Find the center and radius of the circle whose equation is + (y + 2)^ = 25.

10. P is the center of the circle. What's wrongwith this picture? y

4,6

fl(5,-5) /C(l6,-3)

Discovering Geometry Procf/ce Your Skills

02008 Key Curriculum PressCHAPTER 9 63

»7

rs

Name.

Extra Practice

Chapter 3

Lesson 3-1

Use the cubc to name each of the rollowing.

1. all lines that are parallel to BC

2. a pair ofparallel planes

3. two lines that are skew to

.Class

Identify all pairs of each type of angles in the diagnim.Name the hvo lines and the transversal that form eaeh pair.

4. corresponding angles

5. allcmaie interior angles

6. same-side interior angles

7. allemalc exterior angles

Lesson 3-2

Find mZl and mZ.1. State the theorems or postulates (hat justify your answers.

8.

1\2. 46°

10.

. Dale.

H

B

✓

2

50V^

Find the value ofcach variable. Then find the measure of each labeled angle.

16.

tr+1S°(2jt-30')

0(-24''

(3X+34)'' /

(3y-35)yf ' •

5*® If

Prentice Hall Geometry • Extra PracticeCopyrght ® by Pearson Education, Inc., o' its affiliates. AllRights Rcsorvod.

I&

Name Class. . Date.


Chapter 3

17. Complete the proof.

Given: ^ m,a

Prove; Z\ = Z5

Statements Reasons

1. f m,a\b 1. Given

2. Zl = Z2 a._?_

3. Z2 and Z3 are supplementary. b._?_

4. Z3 and Z4 are supplementary. c._?_

5. Z2 = Z4 d-_?_

6. Zl = Z4 e-_?_

7. Z4 s Z5 * _?_

8. Zl = Z5 g._?_

Lesson 3-3

Refer to the diagmm at the ri^jht. Use (he given information todetermine which lines, if any, must be parallel. If any lines are

parallel, use a theorem or postulate to tell why.

18. Z9 s Z14

20. Z2 is supplementary to Z3.

22. mZ6 = 60, mZU = 120

24. Z3 is supplementary to ZIO.

25. Zl = Z8

Find the value ofjc for which a || b.

27. . b

63'

19. Zl = Z9

21. Z7 a ZIO

23. Z4 a Z13

25. ZIO = Z15

a (2x+27)°y'

(S*+3)'

30. Complete the flow proofbclow.

Given; Zl is

supplementaryto Z2

Prove: ( m

(3X-27)

^1 and ^:2bibs(dpI.

Oef.ofUnearpair

{2X+2

d. ?

SupfXementsofthesame^aie:

tI^ and^3 are Hjppl.

t ?

Prentice Hail Geometry • Extra PracOceCopyright® by Pearson Education, Inc., or Its affiliates. All Rights Rssorvod.

a. ?

Lesson 2.6 • Special Angles on Parallel Lines

Name Period

For Exercises 1-3, use yourconjectures to find each angle measure.

1- / 2. i i 3.

For Exercises 4-6, use your conjectures to determine whether ||and explain why. If not enough information is given, write "cannotbe determined."

7. Find each angle measure.

8. Find x

3*- 160°



9. Find x and y.

182' - 4X

5* + 2

Date

CHAFTift2 15

20

Name .Class


Chapter 3

Lesson 3-4

31. Given: I m,a

Prove: b±m

32 Write a paragraph proof.

Given: a b,aK,h±m

t 1

a

"1 , h

m 1 3 , 4

0

.

Prove: e m

Lesson 3-5

33. Use the fieure at th^nght. What is the relationshipbetween ^and Df'l Justify your answer.

Find mA\.

Find the value of each variable.

37. 38.

noy2}C 4/-

Lesson 3-6

Use the segments for each construction.

40. Construct a square with side length 2a.

41. Construct a quadrilalcral with one pair ofparallel sides each of length 2b.

42. Construct a rectangle with sides b and <7.

m

-Date_

Prentice Hall Geometry * Extra PracticeCopyright S by Pearson Education, Inc., or ils affiliates. AllRights Reserved.

10

1\

Name Class Date


Chapters

Lesson 3-7

Use the given inrormation to write an equation of each line.

43. slope -4, y-intercepl 6 44. slope 7, passes through (1, -2)

Write an equation in point-slope form of the line that contains the given points.

45./((4, 2), 5(6,-3) 46. C{-1,-!),/)(!, 1) 47. F(3,-5), G{-5,3)

Write an equation in slope-intcrccpt form of (he line (lirough the given points.

48.A/(-2,4),A'(5,-8) 49./'(0,2), <2(6, 8) 50. ^"(5,0),/,(-5, 2)

Lesson 3-8

Without graphing, tell whether the lines arc parallel, perpendicular, or neither.Explain.

51. y = 4j:-8 52. I3;;_x = 7 53. y= — x + 23

V

3'

' = 7-y=x 42 ^>- = *-1

54. 2i: + 3>'=5 S5.y = -2x+7 56. 5.!C - 3>'= 05

3'5x-10v = 30 x-2y=8 y = ~x + 2

Write an equation for the line parallel to the given line through the given point.

57.3' =a:-7, (0,4) 58. ;'=1a:+3,(6,3) 59.^ =̂ 1^,(5,-8)

Write an equation for the line perpendicular to the given line through the givenpoint.

60.y =Jt +2,(3,2) 61.y -(4,0) 62. =|jr-|,(5,-l)

63. On a city map, Washington Street is stmighl and passes through points at (7, 13) and(1,5). Wellington Street is straight and passes through points at (3,24) and (9,32).Do Washington Street and Wellington Street intersect? 1low do you know?

Prentice Hall Geometry • Extra PracticeCopyright e by Pearson Ei^jcstion. Inc.. or itsaRilialos. All Rights Reserved.

11

2Z

A Name:Parallel and Perpendicular Lines

21. Graph ;' = -;c + 4

Write an equation and graph a line parallel to theabove equation passing through the point (0, -2)

Equation:

•

2. Graph y=̂ x+3

Wrile an equation and graph a line parallel to theabove equation passing through the point (0, -4)

Equation:

3. Graph y = 2x+i

Write an equation and graph a line parallel to theabove equation passing through the point (0, -1)

Equation;

2S

34. Graph =

Write an equation and graph a lineperpendicular to the above equation passingthrough the point (0, -1)

Equation:

<

—

-• •

• -

5. Graph y'=~2x + 4

Write an equation and graph a lineperpendicular to the above equation passingthrough the point (0,4)

Equation:

26. Graph y = -~x + l

Write an equation and graph a lineperpendicularto the above equation passingthrough the point (0,1)

Equation:

o2o

ip

c

i

aI

uM

oo

m

(A01

S

I©IOS5 TJP. in

T K

Im88io

(

Is The Biggest PTcl/]mCircle the number-letterpair of each TRUEstatement. For these pairs, write the letterin the matching numbered box at the right.

I. Use the figure below, inwhich^You should find 11 true statements.

7-E EF intersects AD at C.

11-0r» . *-

EB L AC

2-H FC 11 HG

17-El'hc'xW

1-T

3-A

16-8

12-A

18-G

3-E

8-T

16-E

14-P

4-Y

18-T

6-L

EB II CH

BG J. CH

^11^

ZEBC is a right angle.

LDCE\s a right angle.

mZWCe = 90°.

ZFCH is an acute angle.

LECH is an obtuse angle.

ZABE IS an acute angle.

Perpendicular lines intersect to form right angles.

Parallel lines never intersect.

mZDCH=mZEBH

1 2 3 4 5 6 7 8 g 10 11 12 13 14 15 16 17 18

4th Street

> 5th Street<

6th Street

~1 r

J

II. Use the figure above. You should find 4true statements.

13-L

6-G

10-S

15-F

9-N

10-C

5th Street is parallel to 6th Street.

6th Street is perpendicular to Elm Avenue.

Elm Avenue is parallel to Disk Drive.

4th Street and Oak Avenue intersect toform right angles.

Elm Avenue is perpendicular to Oak Avenue.

Elm Avenue is parallel to Oak Avenue.

(

Constructions:

i. 1 Basic Constructions

When we do consirucllons in geometry, we will use the traditional approach that uses onlyTWO instruments, a compass and a straightedge. Since a compass measures the radius of acircle, and radii ofa circle are congruent, then we can use it to construct congruent segments.A straightedge is used to connect to points. A ruler may not be used to measure distances inconstructions.

Definition: An arc Is any part of a circle.

When we draw using a compass we will be \ drawing arcs. We rarely need tocomplete the entire circle. The radii will still be congruent even if a complete circle is notpresent.

CONSTRUCTION I: Consiruci a segment congruent to a given segment.

Copy AB1. Use the straightedge to draw a line and labelit/.

Choose any point on / and label it C.

B

2.

3.

4.

Set the compass at A and measure the radius ABKEEP1"NG the SAME setting, put the compass atC and draw an arc that intersects line /. Call this

point D.

5. CD = AB

c DW

CONSTRUCTION 2: Construct and angle at a givenpoint congruent to a given angle.Given ZC, copy ZC at F.1. Set compass at C and draw a convenient arc that

intersects both sides of ZC. Label the intersections D

and E.

2. Keeping the same setting, put the compass at Fanddraw the arc intersecting line I at H.

3. Set the compass at D and measure DE.4. Set the compass at //and draw an arc intersecting the

previous arc. Label this point G.

5. Use a straightedge to draw FG.6. ZECD = ZGFH

H

-1-

26

CONSTRUCTION #3: Construct the bisector oj an angle.1. Set the compass at G, draw any convenient arc that

intersects the sides of ZG. Label these points H andK.

2. Set the compass at H and draw an arc that is insideZG.

3. Use the same setting, put the compass at K and drawan arc that intersects the previous arc. Label this L.

4. Use a straightedge to draw GL.5. ZHGL = ZLGK

ASSIGNMENT:

1. Draw a line segment congruent to AB on line a.

a

B

2. Draw a line segment congruent to CD on line b.

C D

3. Draw an angle congruent to ZA at Fon line c.

-2-

17

Documents

Geometry Support Packet Unit 1 - Mater Academy Charter