GeometryMidyearExamReview

1. TriangleABChasverticesA(-2,2),B(0,6),andC(7,5).a)If𝐵𝐷####isanaltitude,finditslength.b)𝑋𝑌####isthemidsegmentparallelto𝐴𝐶####.FindthecoordinatesofXandY.

2. TriangleDEFhasverticesD(2,-4),E(5,0),andF(-2,2).PuttheanglesD,E,andFinorderfromsmallesttolargest.

3. Inthediagramtotheright,solveforx.

4. Whichofthefollowingrepresentalinethatintersectstheline2y+3=5x?A.𝑦 = *

+𝑥 + ./

+

B.5𝑥 − 2𝑦 = 6C.𝑦 − 1 = *

+(𝑥 + 4)

D.𝑦 = − 8+𝑥 + *

+

5. Whichofthefollowingrepresentalineperpendiculartoy=2x+7?I.y=2x-7II.y=−9

+𝑥 − /

+

III.𝑦 + 5 = −9+(𝑥 + 3)

A.Ionly B.IIonly C.IIandIII D.Noneoftheabove6. PointPpartitionsdirectedsegment𝐴𝐵####intheratioof3:4.IfAisat(-9,-9)andBis(5,-2),findthe

coordinatesofP.A.(-3,-7) B.(-3,-6) C.(-6,-6) D.(-4,-6)

7. PointPdivides𝐴𝐵####sothat;<<== 9

>.IfpointAliesat(2,7)andPliesat(4,6),findthecoordinatesof

PointB.A.(2.4,6.8) B.(12,2) C.(12,12) D.(3.6,6.2)

8. a.DrawarhombusandnameitABCD.Whyisyourfigurearhombus?(Thinkaboutthedefinitionofarhombus)b.Drawdiagonals𝐴𝐶####and𝐵𝐷####.Whatpropertiesdothediagonalsofarhombushave?c.Iftwoconsecutivesidesinaparallelogramarecongruent,istheparallelogramarhombus?Explain.

9. Usethepropertiesofthediagonalsandthedefinitionofarhombustosolveforvariablesmandn.

10. Findx

11. Find𝑚∠𝑓

12. Find𝑚∠𝑖

13. Whichtrianglecongruence

postulate(s)ortheorem(s)couldbeusedtoprove∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐶?

a) SASb) HLc) SSSd) SSAe) Thesetrianglescannotbeproven

congruentwiththegiveninformation.

14. Cisthemidpointof𝐴𝐷;∠𝐶𝐵𝐸 ≅ ∠𝐶𝐸𝐵.Whichtrianglecongruencepostulate(s)ortheorem(s)couldbeusedtoprove∆𝐴𝐶𝐵 ≅ ∆𝐷𝐶𝐸I. SSSII. SSAIII. AASIV. HL

a) IIIonlyb) IVonlyc) IandIVd) IIandIII

15. Given∠𝐶𝐴𝐵 = ∠𝐷𝐵𝐴 = 90H;𝐴𝐶#### ∥ 𝐵𝐷####;𝐴𝐸#### ≅ 𝐵𝐸####a) Whichtrianglecongruencepostulate(s)or

theorem(s)couldbeusedtoprove∆𝐶𝐴𝐵 ≅∆𝐷𝐵𝐴?

b) Whichtrianglecongruencepostulatesortheorem(s)couldbeusedtoprove∆𝐶𝐸𝐴 ≅∆𝐷𝐸𝐵

16. Whichwouldnotbesufficienttoprovethetrianglescongruent?a) ∠𝐵 ≅ ∠𝐸b) ∠𝐴 ≅ ∠𝐷c) 𝐶𝐴#### ⊥ 𝐵𝐴####;𝐹𝐷#### ⊥ 𝐷𝐸####d) 𝐴𝐶 = 𝐷𝐹

17. Whichpointisthecircumcenterofr𝐴𝐵𝐶?Justifyyourreasoning.

18. Constructtheincenterofr𝐿𝑃𝑄.

19. Given:rARG,median𝑅𝐿####,centroidE,andaltitude𝑅𝐵####If𝐵𝐿 = 7,𝑅𝐵 = 24,findEL.

20. Constructthemedianfrom𝐹toside𝐴𝑄.

21. Foranobtusetriangle,whichpointsofconcurrencyarelocatedoutsidethetriangle?

Thefollowingtwoquestionsrefertor𝐼𝐵𝑅below:

22. 𝑁𝑉isamidsegment.Whichofthefollowingisatruestatement?Selectallthatapply.

a.Thelengtho𝐼𝐵istwicethatof𝑁𝑉. b.𝐵𝑂 = 𝑂𝐼 c.𝑅𝑉 = 𝑅𝑁 d.𝑁𝑉and𝐵𝐼areparallel e.𝐵𝑁 = 𝑁𝑅

23. 𝑂𝑉isamidsegment.Whichofthefollowingisatruestatement?Selectallthatapply a.Thelengthof𝐵𝑅istwicethatof𝑂𝑉 b.𝐵𝑂 = 𝐵𝑁 c.𝑅𝑉 = 𝑅𝑁 d.𝐵𝑅and𝑂𝑉areparallel e.𝑁𝑉and𝑂𝑁areparallel

24. Inthediagrambelow,Disthemidpointof𝐶𝐸,Bisthemidpointof𝐴𝐶,andFisthemidpointof𝐴𝐸.Let𝐴𝐸 = 𝑥+ − 3𝑥 − 14and𝐵𝐷 = −2𝑥 + 21.Find𝐴𝐸and𝐵𝐷.

25. Findthemeasureofeachexteriorangleof

a. aregularhexagon.b. Aregular17-gon

26. Giveanexpressionforthedifferencebetweenthemeasureofanexteriorangleandthemeasureof

aninteriorangleofaregularn-gon.27. Givenapointonaline,constructtheperpendiculartothelineatthegivenpointP.

28. Constructthelinethatisperpendicularto andthatpassesthroughpointP.

29. ConstructthealtitudefromBto for∆ABC.ConstructthealtitudefromvertexAto for∆ABC.

30. Whichpointofconcurrencyisequidistantfrom:a)thethreesidesofatriangle?b)thethreeverticesofatriangle?c)creates6triangleswithequalarea?

31. Whichpointofconcurrencyisa)theintersectionofthemediansofthetriangle?b)theintersectionofthealtitudesofthetriangle?c)theintersectionoftheperpendicularbisectorsofthetriangle?d)istheintersectionoftheanglebisectorsofthetriangle?e)thecenterofacircumscribedcircle?f)thecenterofaninscribedcircle?

32. Always/Sometimes/Nevera)Thecentroidis______________inthetriangle.b)Thecircumcenteris_____________inthetriangle.c)Theincenteris______________outsideofthetriangle.d)Theorthocenteris_____________onthetriangle.

AC BC

33.

34.

35.

36.

37.

38.

Forthefollowing,(figuretotheleft)showworkalgebraically.a)IfAP=x2andPU=6x,findallpossiblevalue(s)ofx.b)IfBP=w2–32andPV=w–4,findallpossiblevalue(s)ofw,BP,andPV.c)IfCW=2k2–5k–12andCP=k2–15,findallpossiblevalue(s)ofkandPW.

39.

40.

41.

42.

43. ABCDisaparallelogram.Whichofthefollowingconclusions,ifany,is/arenecessarilytrue?(Theremaybemorethanone!)

44.

45. Suppose𝑋𝑌VVVVV⃗ bisects∠𝑍𝑋𝑊.Findallpossiblevaluesof𝑚∠𝑍𝑋𝑊if𝑚∠𝑍𝑋𝑊 = 12𝑥 + 14and𝑚∠𝑌𝑋𝑊 = 𝑥+.