Geometry SOL Practice Test — Set 3 of 6
Set 3 of 6 — 50 more free Geometry SOL practice questions from official VDOE released tests.
1. Triangle ABC is reflected to form A′B′C′ across the line y = x. Which transformation produces A′B′C′?
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Answer: D — reflecting ABC across the line y = x
2. A plumber bent a flexible joint to form an angle of 136°. Another pipe was attached so that points A, B, and D lie on a straight line (forming a straight angle of 180°). Angle x is the angle between the second pipe and the flexible joint, forming a linear pair with the 136° angle. What is the value of x?
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Answer: B — 44
3. Which pair of angles is supplementary (their measures add to 180°)?
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Answer: A — 35° and 145°
4. Lines l and m are parallel. Line t intersects both lines, forming angles labeled ∠1 on line l and ∠2 on line m. Angle 1 and Angle 2 are on opposite sides of the transversal and outside the two parallel lines. Which best describes the relationship between ∠1 and ∠2?
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Answer: J — Alternate exterior angles
5. A straight line l intersects four other lines w, x, y, and z. The angle formed between line l and line w is 110°. The angle between line l and line x is 65°. The angle between line l and line y is 75°. The angle between line l and line z is 115°. Which two lines are parallel?
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Answer: B — x and z
6. Two horizontal lines a and b are cut by a transversal. At one intersection, the angle measure is (4x − 30)°. At the corresponding position on the other line, the angle measure is (2x)°. Which value of x will make line a parallel to line b?
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Answer: G — 15
7. Lines LM and QR are parallel. A transversal intersects LM at point N and QR at point P. Angles ∠M and ∠L are corresponding angles whose measures add to 60°. What is the measure of ∠QNP?
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Answer: B — 120°
8. Two lines l and m are cut by a transversal. Angles are labeled x°, y°, z°, and w° at the intersections. Which additional piece of information would verify that l ∥ m?
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Answer: J — x = w
9. Points R, S, Q, and T are shown. A line AB is given. One of the points lies on the line perpendicular to AB that also bisects AB. Which point lies on that perpendicular bisector?
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Answer: C — S
10. Angle PQR is given. Points A, B, C, and D lie inside the angle. One point lies exactly on the angle bisector of ∠PQR. Which point lies on the bisector of ∠PQR?
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Answer: H — C
11. A construction diagram shows arcs drawn from two points on a line that intersect above the line, forming the standard construction used to copy an angle. The drawing shows the arcs used to construct —
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Answer: B — an angle congruent to a given angle
12. A diagram shows three overlapping sets labeled “cat owners,” “dog owners,” and “fish owners.” The overlap shows that dog owners and fish owners overlap, but cat owners do not overlap with fish owners. Based strictly on this information, which is a valid conclusion?
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Answer: B — No dog owners also own fish.
13. Consider the following statements: p: The sum of two angles is 90°. q: The two angles are complements. Which of the following is a symbolic representation of the statement: “If two angles are not complements, then the sum of the two angles is not 90°”?
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Answer: F — ¬q → ¬p
14. Given: AD ≅ AC and AB ≅ AE. Points D and E lie on opposite sides of point A, forming triangles △ADB and △ACE. Which proportion is true?
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Answer: B — AB / AD = AE / AC
15. Given: △LMQ ≅ △LNP. Which conclusion must be true?
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Answer: B — MN = QL
16. In △PQR, the side lengths are: PQ = 56 mm, QR = 64 mm, PR = 70 mm. From smallest to largest, the angles of △PQR are —
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Answer: F — ∠R, ∠Q, ∠P
17. Which set of lengths could not be the lengths of the sides of a triangle?
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Answer: C — 4 cm, 5 cm, 9 cm
18. The locations of three water pumping stations form a triangle. Distance AB = 650 m Distance BC = 558 m Distance AC =? Which statement describes the possible length of AC?
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Answer: H — between 92 m and 1,208 m
19. The top of a ladder rests against a building 12 feet above the ground. The bottom of the ladder is 5 feet from the base of the building. What is the length of the ladder?
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Answer: C — 13 ft
20. A design is formed by joining isosceles right triangles (45°–45°–90°) and 30°–60°–90° triangles. The hypotenuse of the 30°–60°–90° triangle is 12 cm. Which is closest to the length of one leg of the isosceles right triangle?
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Answer: F — 6 cm
21. A circle has a diameter drawn horizontally. From one endpoint of the diameter, a radius is drawn making a 45° angle with the diameter. What is the diameter of the circle?
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Answer: C — 6√2 in.
22. Quadrilateral ABCD is a parallelogram. Angle A measures 22°. What is the measure of ∠C?
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Answer: F — 22°
23. The vertices of parallelogram ABCD have coordinates A(1, 8), B(4, 2), and C(−2, 7). What are the coordinates of D?
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Answer: A — (−5, 3)
24. A piece of plywood is cut in a straight line from point C to point E to form a desktop. Which measurement would ensure that the desktop is rectangular?
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Answer: J — DE = CA
25. Which of the following is not true about a parallelogram?
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Answer: D — Any two consecutive angles are complementary.
26. A pentagon has five interior angles. Four of them measure 90°, 90°, 100°, and 105°. What is the value of the fifth interior angle x?
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Answer: G — 155°
27. A regular polygon has a central angle x. Which is closest to the measure of x?
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Answer: C — 50°
28. A regular polygon is shown. What is the measure of each interior angle?
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Answer: J — 144°
29. In circle P, LO is a diameter. Points L, M, and O lie on the circle, forming triangle LMO. What is m∠LMO?
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Answer: D — 90°
30. Two secants PB and PD intersect a circle at points A and C, respectively. PA = 5, AC = 4, and PB extends beyond the circle so that PB = 12. What is the length of PC?
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Answer: F — 3
31. In a circle, m∠RPQ = 50° and m∠PRQ = 60°. What is the measure of arc PR?
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Answer: D — 140°
32. A tepee is shaped like a right cone with a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas is needed to cover the tepee (lateral surface area)?
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Answer: F — 581 sq ft
33. The Great Pyramid at Giza has a square base with side length 230 meters and a height of 146.7 meters. Approximately what is the volume of the pyramid?
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Answer: B — 2,590,000 m³
34. The ratio of the circumferences of two circles is 3:2. The radius of the smaller circle is 8 inches. What is the radius of the larger circle?
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Answer: J — 12 inches
35. Two ships leave the same marina at the same time. After 2.5 hours, they are 3.2 miles apart. They continue traveling at the same speed and direction. How far apart will they be 2 hours later?
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Answer: C — 5.76 mi
36. Triangle XYZ is obtained from triangle ABC by a rotation about point P. The rotation is 90° clockwise about the origin. Which of the following indicates the correspondence of the vertices?
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Answer: G — A → Y, B → Z, C → X
37. A figure on a coordinate plane is symmetric left-to-right across the y-axis but not symmetric across the x-axis. This figure is apparently symmetric with respect to —
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Answer: B — the y-axis only
38. A line is graphed on a coordinate plane. It rises 1 unit for every 3 units it moves to the right. What is the most likely slope of the line?
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Answer: F — 1/3
39. Lines ℓ and m are cut by transversal n. Which statement would prove that ℓ ∥ m?
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Answer: A — m∠2 = m∠6
40. Two parallel lines are cut by a transversal. If the measure of ∠1 is 115°, what is the measure of the corresponding interior angle on the same side of the transversal?
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Answer: G — 65°
41. A construction shows a line segment with two arcs drawn from each endpoint intersecting above and below the segment, followed by a straight line drawn through the arc intersections. Which construction is illustrated?
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Answer: J — The perpendicular bisector of a given segment
42. A regular polygon has equal sides and equal interior angles. Each exterior angle measures 60°, and each interior angle is supplementary to its exterior angle. What are the measures of x and y, where x is the exterior angle and y is the interior angle?
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Answer: C — 60°, 120°
43. What is the converse of the following statement? “If Joe goes fishing, then he needs bait.”
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Answer: A — If he needs bait, then Joe goes fishing.
44. Let p represent “x² = 21” and let q represent “x is not a whole number.” Which represents the statement: “If x is a whole number, then x² ≠ 21”?
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Answer: C — ¬q → ¬p
45. Which pipe lengths could be joined to form a triangle?
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Answer: B — 13 ft, 12 ft, 5 ft
46. Joseph is standing 12 feet from a mirror lying flat on the ground. His eyes are 5 feet above the ground. The mirror creates congruent angles of incidence and reflection. A building is 264 feet from the mirror. Which is closest to the height of the building?
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Answer: G — 110 ft
47. In triangle ABC, ∠A = 60° and ∠B = 50°. Which best describes the possible length of side BC relative to sides AB and AC?
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Answer: B — Between 10 and 12 inches
48. The following relationships are shown: Some flowering plants are bushes. Roses are a type of flowering plant. Which statement must be true?
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Answer: J — Some flowering plants are bushes.
49. From a point 12 feet from the base of a building, the angle of elevation to the top is 70°. Given: sin 70° = 0.940 cos 70° = 0.342 tan 70° = 2.75 Which is closest to the height of the building?
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Answer: C — 35 ft
50. Two squares share a vertex. Square ABCD has diagonal AC = 28 mm. Square DECF is congruent to ABCD. What is the perimeter of square DECF?
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Answer: J — 56 mm
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.