Chapters 1–2 115

1–2Cumulative Review

for Chapters

1. How should the angle be written?Q

R P

A. /PQRB. /RQPC. /QRPD. /P

2. WhichmeansJKisalinesegment?

J K

A. <JK>

B. JK>

C. JKD. JK

3. If angle Lis217°,whatquadrantisitin?

A. Quadrant IB. Quadrant IIC. Quadrant IIID. Quadrant IV

4. Whataretheverticesofthereflectionofthefigureaboutthey-axis?

y

x–5–6 –4 –3 –2 –1

–5–6

–4–3–2–1

56

4321

5 64321

A. (5, 2), (3, 1), and (1, 2 2)B. (25, 22), (23, 21), and (21, 2)C. (5, 22), (3, 21), and (1, 2)D. (22, 5), (21, 3), and (2, 1)

5. /XYZmeasures41°.Itisrotated2°.Aftertherotation,itsmeasureisA. 43°iftherotationisclockwise,39°ifthe

rotation is counterclockwise.B. 39°iftherotationisclockwise,443°if

the rotation is counterclockwise.C. 41°D. 82°

6. Whichofthefollowingisthereflectionofthe point (24, 7) across the line x 5 1?

A. (24, 27)B. (24, 25)C. (4, 7)D. (6, 7)

7. Twolinesarenotparallel.Thismeans

A. Theycannotbeinthesameplane.B. Theymustintersect.C. Thetwolinesmustdefineaplane.D. Theymayormaynotbeinsameplane.

8. A triangle is dilated by a scale factor of 1.5 and then by a scale factor of 0.8. The resultingfigureis

A. No longer a triangle.B. Larger.C. Smaller.D. Thesamesize.

9. Aparallelogram(afour-sidedfigurewithsidesthatareparallel)isreflected,rotated,reflectedagain,andthentranslated.Theresultingfigureis

A. Notaparallelogram.B. Aparallelogramthatislarger.C. Aparallelogramthatissmaller.D. Aparallelogramofthesameshapeand

size.

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116 Cumulative Review

10. Whatisthereflectionofthepoint(24, 22) about the y-axis?

11. /ABCisdividedbyalinecontainingpointD.Giventhatthemeasureof/ABD is four timesaslargeasthatof/CBD, and the productofthemeasuresofthesetwoanglesis169,whatistheexactmeasureof/ABC?

12. MP 1 Youhaveanunlimitednumberof17°and13°angles.Youcanaddorsubtracttheseanglestomakenewanglesofdifferentsizes.Forexample,youcanadda17°angleanda13°angletomakea30°angle,orsubtracta13°anglefroma17°angletomakea4°angle.Explain how you can use these angles to createananglewithameasureof29°.

13. nABC , nDEF.WhatisEF?

B C

A

E F

D

4.5

6

12

14. Thetwotrianglesshownbelowaresimilarand drawn so corresponding sides are in the samelocations.Whatisa?

a b

16

618

24

15. ThecoordinatesofvertexX of triangle XYZ are (21,25).FindthecoordinatesofX9 if the triangle is dilated by a scale factor of 5 and if the center of dilation is the origin.

16. ThecoordinatesofvertexX of triangle XYZ are(6,0).FindthecoordinatesofX9 if the triangle is dilated by a scale factor of 6 and if the center of dilation is the origin.

17. ThecoordinatesofvertexX of triangle XYZ are (27,6).FindthecoordinatesofX9 if the triangle is dilated by a scale factor of 6 and the center of dilation is the origin.

18. Writethepossiblesidelengthsofatrianglethatissimilartotheoneshownbelow.

9 in

8 in7 in

19. Graph nQUA,whichhasverticesat Q(22, 1), U(1, 5), and A(3, 1). Then, graph nEGO,whichistheresultofarigidmotiontransformationofnQUA.Labeltheverticesof both triangles.

20. Usethecompassrosetoanswer the following questions.

a Ifthecompassrosecontinuestopointinthesamedirectionbutisfoundinadifferentlocation on the page, what type of rigid motionhasoccurred?

b Ifthecompassroseismovedinasingle transformationsuchthatN and S exchange positions and E and W exchange positions, what type of transformationhasoccurred?

c If the area of the black sections of the compassroseistobeincreasedbya factorof4,whattypeoftransformationhasoccurred,andbywhatamount?

Exercises21–22:WhatisthedistancefromP to P9?

21. Point P has coordinates (6, 23) and P9 is its reflectionacrossthelinex 5 22.

22. Point P has coordinates (8, 26) and P9 is its reflectionacrossthelinex 5 21.

23. a Do dilations change the interior angles of afigure?Explain.

b Doesanytransformationdiscussedsofarchange the angles of a triangle?

24. Point H lies on BK. BK is 84 and BH is 8. WhatisHK?

25. Draw a triangle. Construct a congruent triangleusingacompass,ruler,andprotractor. Label the side lengths and angle measuresofeach.

N

W E

S

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Chapters 1–2 117

26. Youwanttomoveafigure3totheleftandup2.Whatconstantsdoyouaddtothecoordinates of each point?

27. nABC > nZYX. If m/B=80° and m/C=10°,whatdoesZ equal? Hint:ConsiderwhatangleZ corresponds to inΔABC.

28. Theratiooftheperimeterofoneequilateraltriangletotheperimeterofanotherequilateraltriangleis1:4.Howmanyofthesmallertriangleswouldfitinsidethelargertrianglewithnooverlaporuncoveredspace?

29. Triangle ABCisdilatedtoformtriangle

A′B′C′.Sophiacalculatestheratio ABA rB r

to

be 5 and states that the scale factor for this dilation is 5. Is Sophia correct? Explain.

30. MP 5, 7 Triangle ABChasverticesat(1,4),(5, 21), and (22, 27).

a Graph the triangle. b Nameatransformationthatproducesa

figurethatisbothcongruentandsimilar.Describethetransformationandgivethecoordinates of the new triangle. Draw the newtriangleonthesamecoordinateaxisas the original.

c Nameatransformationthatproducesafigurethatisnotcongruentbutsimilar.Describethetransformationandgivethecoordinates of the new triangle. Draw the newtriangleonthesamecoordinateaxisas your other two.

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