Download Geometry Quarter 2 Benchmark Review

Name: ______________________ Class: _________________ Date: _________
ID: A
Geometry Quarter 2 Benchmark Review
Short Answer
Use the figure below.
1. What is another name for line m?
2. Name the intersection of planes A and B.
3. Find the length of DE.
Use the coordinate grid.
4. Find the distance between L and M.
5. The vertices of a triangle are located at P(0, 6), Q(8, 12), and R(3, −3). What is the perimeter of this
triangle?
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Name: ______________________
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ID: A
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In the figure, RC and RD are opposite rays and RQ bisects ∠WRV.
6. Find y if m∠WRQ = 48 and m∠QRV = 7y + 6.
Use the figure below.
7. Find x.
8. Find m∠1.
Refer to the figure.
9. Identify the intersection of plane ABD and plane CDE.
10. Name a segment skew to BC.
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive
interior angles.
11. Find x and y given a Ä b, m∠8 = 4x + 10, m∠12 = 7x − 17, and m∠11 = 3y.
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Name: ______________________
ID: A
Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
12. ∠QSR ≅ ∠SUT
13. Find x so that p Ä q.
Find the distance between each pair of parallel lines.
14. y = 3x − 1 and y = 3x − 11
15. y = −5x and y = −5x + 26
16. Find x, AB, BC, AC if
ABC is isosceles.
17. Find the measure of the sides of the triangle if the vertices of
Then classify the triangle by its sides.
Find the measure of each angle.
18. m∠1
19. m∠2
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EFG are E(1, 4), F(5, 1), and G(2, −3).
Name: ______________________
ID: A
20. Identify the congruent triangles and name their corresponding congruent angles.
21. Find m∠1.
22. Find x.
23. Name a perpendicular bisector.
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24. The perimeter of PRQS is 34. Find x. Then describe the relationship between RS and PQ.
25. If point N is the centroid of
HIJ, IM =18, KN = 4, and HL = 15, find JN.
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Name: ______________________
26. If RU is an altitude for
ID: A
RST, find x.
27. A rubber doorstop has a hypotenuse measuring 7z and a height measuring x − 5. Write an inequality
relating x and z.
28. List the angles of
TUV in order from least to greatest measure.
29. Name the longest segment.
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30. Find the shortest distance from B to AC .
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31. If YW bisects ∠XYZ, find x.
32. A convex octagon has interior angles with measures (x + 55)°, (3x + 20)°, 4x°, (4x − 10)°, (6x − 55)°,
(3x + 52)°, 3x°, and (2x + 30)°. Find x.
33. If the measure of each interior angle of a regular polygon is 176 find the number of sides on the
polygon.
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Name: ______________________
ID: A
34. In parallelogram ABCD, m∠1 = x + 25, and m∠2 = 2x. Find m∠2.
35. Find the coordinates of the intersection of the diagonals of parallelogram XYZW with vertices X(3, 0),
Y(3, 8), Z(−2, 6), and W(−2, −2).
36. If the slope of AB is 1 , the slope of BC is −4, and the slope of CD is 1 , find the slope of DA so that
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ABCD is a parallelogram.
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37. ABCD is a rhombus with diagonals intersecting at E. If m∠ABC = 4m∠BAD, find m∠EBC.
38. PQRS is a square with Q(−2, 8), R(5, 7), and S(4, 0). Find the coordinates of P.
39. For isosceles trapezoid MNOP, find m∠MNQ.
Write true or false.
40. A parallelogram always has four right angles.
41. The diagonals of a rhombus always bisect the angles.
42. A rhombus is always a square.
43. A rectangle is always a square.
44. The diagonals of an isosceles trapezoid are always congruent.
45. The median of a trapezoid always bisects the angles.
46. The measure of each interior angle of a regular polygon is 24 more than 38 times the measure of each
exterior angle. Find the number of sides of the polygon.
47. Of the 112 students in the marching band, 35 were in the drum section. What is the ratio of drummers
to other musicians in the band?
48. Determine whether quadrilateral ABCD ∼ quadrilateral EFGH. Justify your answer.
49. When a 9-foot tall garden shed cast a 5-foot, 3-inch shadow, a house cast a 28-foot shadow. Find the
height of the house.
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Name: ______________________
ABC ∼
50.
ID: A
FGH, AB = 24, AC = 16, GH = 9, and FH = 12. Find the scale factor of
ABC to
FGH.
51. The model of a suspension bridge is 18 inches long and 2 inches tall. If the length of the actual bridge is
1650 feet, find its height.
52. Find GP.
53. If
JKL ∼
PQR, find x.
54. Determine whether
ABC ∼
55.
ABC ∼
PQR. Justify your answer.
PQR, AB = 18, BC = 20, AC = 22, and QR = 25. Find the perimeter of
Use the figure below.
56. Identify the similar triangles.
57. Find MN.
58. If
FGH ∼
LMN and AF and BL are medians, find BL.
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PQR.
Name: ______________________
ID: A
59. If quadrilateral DEFG ∼quadrilateral WXYZ, find m∠Y.
60. In
PQR, QS bisects ∠PQR. Find x.
61. Find x so that PQ Ä FH.
62. If
FGH ∼
JKL, find GX.
63. Find y.
64. Find FG.
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ID: A
Geometry Quarter 2 Benchmark Review
Answer Section
SHORT ANSWER
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1. TU , or UV, or TV
2.
3.
4.
5.
6.
7.
8.
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RS
17 cm
65
10 +
6
7
122
90 +
250 or 10 + 8
10 ≈ 35.3 units
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9. CD
10. Sample answer: AE
11. x = 17; y = 26
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
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RS Ä TU ; corr. ∠s
12
10
26
x = 5, AB = BC = 30, AC = 40
EF = FG = 5, EG = 5 2 , isosceles
110
70
ABC ≅ FDE, ∠A ≅ ∠F, ∠B ≅ ∠D, ∠C ≅ ∠E
50
x=6
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23. LM
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
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x = 5; RS is the ⊥ bisector of PQ.
8
20
7z > x − 5
∠T, ∠V, ∠U
LM
BE
35
38
90
50
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ID: A
ˆ
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Ê
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35. Á 1 , 3 ˜
˜
˜
Ë 2
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˜
¯
˜
36. −4
37. 72
38. (−3, 1)
39. 16
40. false
41. true
42. false
43. false
44. true
45. false
46. 90
47. 5:11
48. No; the corresponding sides and ∠s are not proportional.
49. 48 ft
50. 4
3
51. 183 1 ft
3
5.5
15
Yes; SSS Similarity
75
XYZ ∼ XNM
7.5
2.2
85
9.5
2
62. 5 5
8
63. 28
64. 4.8
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
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