Geometry SOL Practice Test — Set 4 of 6
Set 4 of 6 — 50 more free Geometry SOL practice questions from official VDOE released tests.
1. The opposite sides of a window frame are congruent. Which additional information would verify that the frame is a rectangle?
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Answer: B — Diagonals AC ≅ BD
2. In parallelogram WXYZ, W = (−2, 6), X = (6, 6), Y = (9, 1), and Z = (1, 1). What are the coordinates of the point of intersection of diagonals WY and ZX?
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Answer: J — (3.5, 3.5)
3. For a regular polygon with three sides, each interior angle has a measure of —
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Answer: G — 60°
4. Each interior angle of a regular polygon measures 156°. How many sides does the polygon have?
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Answer: B — 14
5. In parallelogram ABCD, m∠A = 4x° and m∠B = 8x°. If x = 5, what is m∠D?
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Answer: B — 120°
6. A concrete pillar is shaped as a rectangular prism with dimensions 9.5 m by 1.5 m by 15 m. Which is closest to the volume of concrete needed?
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Answer: C — 21.4 m³
7. A right triangular pyramid has a height of 10 inches and a base area of 41.57 square inches. What is the volume, in cubic inches, of the pyramid?
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Answer: G — 207.85
8. The surface area of a plastic ball is 196π. A sponge ball has a radius twice that of the plastic ball. What is the surface area of the sponge ball?
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Answer: C — 784π
9. The diameter of a circle has endpoints (−3, 2) and (3, −2). Which is closest to the length of the diameter?
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Answer: H — 7.2
10. What are the most likely coordinates of R′ if segment R′S′ is a reflection of RS across the y-axis and R is at (−4, 3)?
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Answer: A — (4, 3)
11. A line segment has one endpoint at (3, 2). If the midpoint is (6, −2), what are the coordinates of the other endpoint?
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Answer: J — (9, −6)
12. A ladder is leaning against a vertical house. The angle between the ladder and the vertical side of the house is 38°. What is the measure of the angle between the ladder and the ground?
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Answer: D — 142°
13. Two lines, AB and CD, intersect at point P. Segment PR is perpendicular to line AB. The measure of ∠APD is 170°. What is the measure of ∠DPB?
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Answer: A — 10°
14. In triangle ABC, sides BC and AC are extended to form two sides of parallelogram CDEF. The measures of ∠CAB and ∠CBA are each 36°. What is the measure of ∠CFE?
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Answer: C — 72°
15. Line a is parallel to line b. Which condition proves the lines are parallel?
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Answer: C — m∠4 = m∠5
16. Triangle ABC is a right triangle with the right angle at C. Which are possible measures for angles A and B?
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Answer: C — 52° and 38°
17. If negotiations fail, the baseball strike will not end. If the baseball strike does not end, the World Series will not be played. Which conclusion logically follows?
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Answer: D — If negotiations fail, the World Series will not be played.
18. Let a represent “x is an odd number.” Let b represent “x is a multiple of 3.” When x = 7, which statement is true?
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Answer: B — a ∧ ¬b
19. Given AC ≅ BD, which postulate could be used to prove △DCA ≅ △CDB?
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Answer: A — SSS
20. On the shores of a river, three points A, B, and C are marked. The measure of ∠ACB is 70°, and the measure of ∠ABC is 65°. Which lists the distances between the locations in order from least to greatest?
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Answer: C — B to C, A to C, A to B
21. Triangles ABC and EFG are similar. Side AC corresponds to side EG. The length of AC is 5 units, and the length of EG is 7 units. What is the ratio AC : EG?
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Answer: A — 5 : 7
22. Which of the following could be the lengths of the sides of triangle ABC?
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Answer: D — 10, 8, 12
23. A 20-foot ladder leaning against a building makes an angle of 60° with the ground. How far from the base of the building is the foot of the ladder?
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Answer: C — 10 ft
24. An airplane is 34 miles horizontally from the end of a runway and 6 miles above the ground. To the nearest mile, what is the distance from the airplane to the end of the runway?
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Answer: D — 35 mi
25. In a circle with diameter 12 cm, ∠RST is 30°. What is the length of chord SR?
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Answer: C — 6√3 cm
26. Points A(2,3), B(?,?), C(5,0), and D(0,0) form a parallelogram ABCD. What are the coordinates of B?
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Answer: D — (7,3)
27. Which quadrilateral could have diagonals that are congruent but do not bisect each other?
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Answer: D — Trapezoid
28. Three vertices of a square are at (5,1), (2,2), and (1,1). What are the coordinates of the fourth vertex?
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Answer: C — (2,4)
29. A regular pentagon has all sides extended. What is the measure of each interior angle of the pentagon?
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Answer: A — 72°
30. Each exterior angle of a regular polygon measures 30°. How many sides does the polygon have?
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Answer: D — 12
31. Triangle ABC is inscribed in a circle. The intercepted arc opposite ∠BAC measures 40°. What is the measure of ∠BAC?
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Answer: D — 20°
32. A scale drawing shows 1 cm represents 13 m. The height of the drawing is 4.5 cm. What is the actual height of the building?
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Answer: A — 58.5 m
33. What is the volume of a refrigerator that is 4.5 feet tall, 2.5 feet wide, and 2 feet deep?
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Answer: C — 22.5 cubic feet
34. Two vehicles move away from each other at a constant angle. After 6 seconds, they are 150 feet apart. Vehicle A travels at 50 ft/s, and Vehicle B at 40 ft/s. How far apart are they after 15 seconds?
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Answer: B — 375 ft
35. A mirror is placed on the ground 25 feet from the base of a tree. A person whose eyes are 5 feet above the ground stands so that the distance from her eyes to the mirror is 3.25 feet and sees the top of the tree. Which is closest to the height of the tree?
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Answer: C — 38 ft 6 in.
36. Quadrilateral ABCD is symmetric with respect to the y-axis. If point B is at (2,1), what are the coordinates of point D?
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Answer: C — (−2,1)
37. If vector RS = (3, −2) and vector TV = (−1, −4), which column matrix represents RS + TV?
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Answer: A — (2, −6)
38. A circle has center (1,3) and passes through the point (7,5). What is the radius of the circle?
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Answer: A — 10
39. Joan drives 3 miles north, 2 miles east, 4 miles north, and 5 miles east. Which vector represents the resultant displacement?
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Answer: C — (7,7)
40. Two parallel lines are intersected by a transversal. One angle formed is 90°, and the angle on the opposite side of the transversal on the other parallel line is labeled x. The given angle adjacent to x on the same intersection is 115°. What is the value of x?
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Answer: C — 135°
41. Parallel lines ℓ and m are cut by transversal c. It is given that the measure of angle 4 equals the measure of angle 5, and the measure of angle 6 equals the measure of angle 7. Which of the following is the measure of the supplement of ∠CAB?
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Answer: D — 142°
42. What are the measures of two complementary angles if the difference of their measures is 18°?
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Answer: A — 36°, 54°
43. Line n intersects lines p, q, r, and s, forming angles. Two of the angles formed with line n are congruent corresponding angles. Which two lines are parallel?
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Answer: B — p and r
44. Which statement will prove that line ℓ is parallel to line m, given a transversal with angles labeled 1 through 7?
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Answer: D — ∠7 = ∠1
45. A construction is shown for drawing a line parallel to QR through point P. Which arc must be drawn first in this construction?
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Answer: A — Arc centered at point P
46. Given m∠1 = 110°. Which must be true if lines y and z are parallel?
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Answer: D — m∠5 = 110°
47. Which two points determine a line parallel to QR, where QR has slope −1?
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Answer: A — (1, 1) and (2, −1)
48. According to a Venn diagram of car features showing overlapping sets for Automatic Transmission, Rear-Wheel Drive, and 4-Cylinder Engine, which statement is true?
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Answer: D — Some cars have automatic transmissions and 4 cylinders.
49. Which set of statements represents an invalid argument?
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Answer: C — If Mark goes camping, then he will go fishing. If Mark goes fishing, then he will buy bait. Therefore, if Mark does not buy bait, then he will go camping.
50. Triangles ABC and EFG are similar. Triangle ABC has sides 5 cm, 6 cm, and 7 cm. Triangle EFG has corresponding sides scaled by a factor of 2. What is the perimeter of triangle EFG?
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Answer: D — 42 cm
Geometry SOL practice test — FAQ
Are these Geometry SOL practice questions free?
Yes — this Geometry SOL practice test is completely free with no signup. Answer each question to check it instantly, or open "Show answer" to review.
How many Geometry SOL practice questions are there?
Across all sets, there are 347 Geometry practice questions drawn from official Virginia Department of Education released SOL tests. This set has 50.
Are these real Virginia SOL questions?
The questions are adapted from official VDOE released SOL tests for Geometry. SOL Prep is an independent study aid and is not affiliated with or endorsed by the Virginia Department of Education.
Practice items adapted from Virginia Department of Education released SOL tests. Practice items are provided for study purposes and are not affiliated with or endorsed by the Virginia Department of Education.