Geometry Common Planning Midyear Review · Geometry Midyear Exam Review 1. Triangle ABC has...
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Geometry Midyear Exam Review 1. Triangle ABC has vertices A(-2, 2), B(0, 6), and C(7, 5). a) If # # # # is an altitude, find its length. b) # # # # is the midsegment parallel to # # # # . Find the coordinates of X and Y. 2. Triangle DEF has vertices D(2, -4), E(5, 0), and F(-2, 2). Put the angles D, E, and F in order from smallest to largest. 3. In the diagram to the right, solve for x. 4. Which of the following represent a line that intersects the line 2y + 3 = 5x? A. = * + + ./ + B. 5 − 2 = 6 C. −1= * + ( + 4) D. =− 8 + + * + 5. Which of the following represent a line perpendicular to y = 2x + 7? I. y = 2x - 7 II. y = − 9 + − / + III. +5=− 9 + ( + 3) A. I only B. II only C. II and III D. None of the above 6. Point P partitions directed segment # # # # in the ratio of 3:4. If A is at (-9,-9) and B is (5,-2), find the coordinates of P. A. (-3, -7) B. (-3, -6) C. (-6, -6) D. (-4, -6) 7. Point P divides # # # # so that ;< <= = 9 > . If point A lies at (2, 7) and P lies at (4, 6), find the coordinates of Point B. A. (2.4, 6.8) B. (12, 2) C. (12, 12) D. (3.6, 6.2) 8. a. Draw a rhombus and name it ABCD. Why is your figure a rhombus? (Think about the definition of a rhombus) b. Draw diagonals # # # # and # # # # . What properties do the diagonals of a rhombus have? c. If two consecutive sides in a parallelogram are congruent, is the parallelogram a rhombus? Explain. 9. Use the properties of the diagonals and the definition of a rhombus to solve for variables m and n. 10. Find x
Transcript of Geometry Common Planning Midyear Review · Geometry Midyear Exam Review 1. Triangle ABC has...
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
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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.
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43. ABCDisaparallelogram.Whichofthefollowingconclusions,ifany,is/arenecessarilytrue?(Theremaybemorethanone!)
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45. Suppose𝑋𝑌VVVVV⃗ bisects∠𝑍𝑋𝑊.Findallpossiblevaluesof𝑚∠𝑍𝑋𝑊if𝑚∠𝑍𝑋𝑊 = 12𝑥 + 14and𝑚∠𝑌𝑋𝑊 = 𝑥+.
