cumulative review for chapters 1–2...chapters 1–2 1151–2 cumulative review for chapters 1. how...
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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.
Chapter 2.indd 115 10/15/14 12:20 PM
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
Chapter 2.indd 116 10/15/14 12:20 PM
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.
Chapter 2.indd 117 10/15/14 12:20 PM
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