Geometry Name_______________________________________________SemesterReviewAChapters1–5,9 MultipleChoice.Choosethebestanswer.1. Findthescalefactorofthedilationthatmaps𝐴𝐵𝐶onto𝐴′𝐵′𝐶′.

A.!

! B.!

! C.!

! D.!

!

2. In∆𝑋𝑌𝑍,thecoordinatesof𝑌are(4, 3).If∆𝑋𝑌𝑍undergoes

thecompositionofthetransformationslistedbelow,whatarethecoordinatesofthefinalimageof𝑌?

Translation:(𝑥,𝑦) → (𝑥 + 2,𝑦 − 4) Rotation:180°abouttheorigin

A.(6,−1) B. (−6,−1) C.(6, 1) D.(−6, 1)3. Whatis𝑚∠𝑇𝑅𝑌?

A.62° B.67° C. 119° D.129°4. Inafigure,∠𝑋and∠𝑌arecomplementaryangles

and𝑚∠𝑋 = (𝑎 + 4)°.Whichexpressioncanbeusedtofind𝑚∠𝑌?

A.[90− 𝑎 + 4 ]° B.[ 𝑎 + 4 − 180]°

C.[90+ 𝑎 + 4 ]° D.[180− 𝑎 + 4 ]°

5. Adilationmaps∆𝐴𝐵𝐶onto∆𝐴′𝐵′𝐶′.Whatisthescalefactorofthedilation?

A.171.5 B.31.5 C.17.5 D.3.56. Whatisthevalueof𝑥?

A.145 B.113 C.35 D.237. Whatisthelengthof𝐴𝐶?

A.3 B.11 C.21 D.778. Basedontheinformationinthefigure,whichstatementshowsavalidargument?

A. 2𝑥 + 9 + 12𝑥 = 180becausetheanglesformalinearpair.

B. 2𝑥 + 9 + 12𝑥 = 90becausetheanglesarecomplementary.

C. 2𝑥 + 9 = 12𝑥becausetheanglesareverticalangles.

D. 2𝑥 + 9 = 12𝑥becausetheanglesaresupplementary.

9. Forthefigurebelow,whatpropertyisusedtomaketheconclusion?

Given:𝑪𝑫 = 𝑩𝑪,𝑩𝑪 = 𝟖 Conclusion:𝑪𝑫 = 𝟖

A.TransitivePropertyofEquality B.DefinitionofCongruentSegments

C.ReflexivePropertyofEquality D.SegmentAdditionPostulate

10. Basedonthefigure,whichconclusioniscorrect?

A.𝑚∠4 = 𝑚∠2becausetheyarealinearpair.

B.𝑚∠4 = 𝑚∠1becausetheyareverticalangles.

C.𝑚∠1 = 𝑚∠3becausetheyareverticalangles.

D.𝑚∠1 = 𝑚∠2becausetheyarealinearpair.

11. Forwhatvalueof𝑥is𝑚 ∥ 𝑛?

A.10 B.20 C.40 D.100

12. Forthreelines,𝑎, 𝑏,𝑎𝑛𝑑 𝑐,𝑎 ∥ 𝑏,and𝑐 ⊥ 𝑎,whichconclusionisvalid?

A.𝑐 ⊥ 𝑏 B.𝑏 ⊥ 𝑎 C.𝑎 ∥ 𝑐 D.𝑐 ∥ 𝑏

13. Whichcongruencetheoremcanbeusedtoshowthat∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴?

A.SSS B.ASA C.SAS D.AAS

14. Whichcongruencetheoremcanbeusedtoshowthatthetrianglesarecongruent?

A.SSS B.ASA C.SAS D.AAS

15. Whichcongruencetheoremcanbeusedtoshowthatthetrianglesarecongruent?

A.SSS B.ASA C.SAS D.AAS

16. Thediagramshowsanexpansionof∆𝑃𝑄𝑅.If𝐶𝑃 = 2 ∙ 𝑃𝑃′,

whatisthescalefactoroftheexpansion?

A.!

! B.!

! C.!

! D.!

!

17. Whattransformationisdemonstratedbythepicture?

A.rotation B.reflection C.translation D.dilation

18. Inthefigure,rectangleBisadilationofrectangleA.Whatis𝑥?

A.3 B.8 C.12 D.24

19. Whatisthelineofreflectionfor∆𝐿𝑀𝑁anditsimage?

A.𝑦 = 0

B.𝑥 = 0

C.𝑦 = 𝑥

D.𝑦 = −𝑥

20. In∆𝐴𝐵𝐶,𝐴isat(4, 2).Whatarethecoordinatesoftheimageof𝐴when∆𝐴𝐵𝐶isrotated 270°clockwiseabouttheorigin?

A. 4, 2 B.(-2,4) C.(-4,-2) D.(-2,-4)21. Whatisthelengthofthesegmentwithendpoints −2, 4 and(6,−2)?

A. 18 B. 68 C.6 D.10 22. Whatisthemidpointofthesegmentwithendpoints 4, 9 and(2, 7)?

A. 6, 16 B.(3,8) C.(2,2) D.(6.5,4.5)23. Whatisthemissingendpointofasegmentwithoneendpointof −3, 1 and

midpointof(3,−11)?

A. 0,−10 B.(6,-6) C.(0,-5) D.(9,-23)24. Atrianglehasverticesat𝐴(1, 2),𝐵(2, 5),andC(8, 3).

Classifythetrianglebyitssidesandbyitsangles.

A.Acutescalene

B.Rightscalene

C.Rightisosceles

D.Acuteequilateral

25. Usearulertofindthelengthofthesegment.

A.3.1cm B.7.5cm C.7.8cm D.8cm

26. Useaprotractorforfindthemeasureof∠𝑉𝑅𝑇?

A.39° B.41° C. 139° D.141°

27. Whatistheperimeteroftherectangle?

A.18.1m B.36.2m C.64m D.66.3m

28. 𝑀isthemidpointofthesegment.Whatisthelengthofthesegment?

A.9 B.10 C.16 D.32

29. Ifthefigureisaregularpentagon,findthevalueof𝑥.

A.5 B.14 C.25 D.70

30. Whatpropertyofrealnumbersisdemonstratedbythestatement? “If𝑥 = 20,then𝑥 + 𝑦 = 20+ 𝑦. "

A.TransitivePropertyofEquality B.SubstitutionPropertyofEquality

C.ReflexivePropertyofEquality D.AdditionPropertyofEquality

31. Whatpropertyofrealnumbersisdemonstratedbythestatement? “If𝑎 = 20,then20 = 𝑎. "

A.TransitivePropertyofEquality B.SubstitutionPropertyofEquality

C.ReflexivePropertyofEquality D.SymmetryPropertyofEquality

32. Whatpropertyofrealnumbersisdemonstratedbythestatement? “If3 𝑥 − 8 = 6,then3𝑥 − 24 = 6"

A.TransitiveProperty B.DistributiveProperty

C.ReflexiveProperty D.IdentityProperty

33. Whatpropertyofrealnumbersisdemonstratedbythestatement? “If𝑥 = 7and𝑦 = −10+ 𝑥,then𝑦 = −3. "

A.TransitivePropertyofEquality B.SubstitutionPropertyofEquality

C.ReflexivePropertyofEquality D.SymmetryPropertyofEquality

34. Whatpropertyofrealnumbersisdemonstratedbythestatement? “If𝐴𝐵 = 𝐶𝐷and𝐶𝐷 = 𝐹𝐺,then𝐴𝐵 = 𝐹𝐺. "

A.TransitivePropertyofEquality B.SubstitutionPropertyofEquality

C.ReflexivePropertyofEquality D.SymmetryPropertyofEquality

FreeForm.Showyourworkandcircletheanswer.34. Inthediagram,𝐵𝐷bisects∠𝐴𝐵𝐶.Whatisthemeasureof∠𝐴𝐵𝐶?

35. Mr.Tsaid,“Iftwoanglesareverticalangles,thentheyarecongruent.Since∠𝐴and∠𝐵arecongruent,theyareverticalangles.”DescribeMr.T’serrorandcorrecttheerror.

36. Thedesignforaroadsignshowsthelayoutforonlyhalfofthesign.

a. Whattypeoftransformationcanadesignerusetocreateplansfortheentiresign?

b.Describethetransformationasaccuratelyaspossible.

c.Completethetransformationyoudescribedabove.37. Sketch,mark,andlabelregulartriangle𝑇𝑅𝐼withperimeter51mwithincenter𝑂andits

inscribedcircle.38. Giveacounterexampleof…”Triangleshaverightangles.”39. Sketchafigurethathas… a.Twolinesofsymmetry b.90°rotationalsymmetry c.Glidereflection

L L

40. In𝑋𝑌,𝑋(0, 5)and𝑌 8,−1 .Graph𝑋𝑌,𝑋′𝑌′,𝑋′′𝑌′′,𝑋′′′𝑌′′′,and𝑋′′′′𝑌′′′′.1st…Translation(slide): −𝟔,−𝟕

𝑋′( , ) 𝑌′( , )

2nd…Dilationabouttheorigin:(𝒙,𝒚)⟶ (𝟏𝟐𝒙, 𝟏

𝟐𝒚)

𝑋′′( , ) 𝑌′′( , )

3rd…Rotationabouttheorigin:270°counter-clockwise

𝑋′′′( , ) 𝑌′′′( , )4th…Reflectionover𝒙 = 𝟎 𝑋′′′′( , )𝑌′′′′( , )41. FindthescalefactorandthecenterofthecontractiondilationoftiltedLs. 42. Chueisrunningaroundthegreenspaceofatriangularpark. Whilerunning,hestartsthinkingaboutgeometryclass.He wonderswherecircumcenterandthecentroidpointswould belocated.Usethegriddedmapoftheparktolocatethe circumcenter(C)andcentroid(T).