Cumulative Review for Chapters 1–2...Chapters 1–2 1151–2 Cumulative Review for Chapters 1. How...
Transcript of Cumulative Review for Chapters 1–2...Chapters 1–2 1151–2 Cumulative Review for Chapters 1. How...
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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