Geometry SOL Practice Test — Set 2 of 6
Set 2 of 6 — 50 more free Geometry SOL practice questions from official VDOE released tests.
1. A figure is composed of a regular pentagon attached to a rectangle along one side. Angles labeled x are the interior angles of the regular pentagon. What is the measure of each angle labeled x?
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Answer: D — 108°
2. Points Q, R, and S lie on circle P. Angle QPS is a central angle measuring (x + 15)°. The intercepted arc QS measures 40°. What is the value of x?
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Answer: H — 25
3. In circle P, m∠HJK = 60°, and the measure of arc JK is twice the measure of arc HJ. What is the measure of arc HJ?
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Answer: B — 120°
4. Circle P has a radius of 1 unit. A central angle of circle P measures 225°. What is the length of the minor arc?
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Answer: C — 3π/4 units
5. The design for an arc-shaped stand is based on a 144° arc of a circle with a radius of 2.3 meters. What is the length of the arc, rounded to the nearest hundredth?
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Answer: C — 5.78 m
6. Three concentric circles share center O. • The radius of the smallest circle is r. • The radius of the middle circle is 2r. • The radius of the largest circle is 3r. • Segment KP, from the center to the outer circle, measures 42 inches. Which value is closest to the area of the shaded region between the middle and largest circles?
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Answer: J — 616 sq in.
7. In circle T, the radius WP is 36 centimeters. A sector of the circle subtends a central angle of 65°. Which best represents the area of the shaded sector?
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Answer: D — 468π cm²
8. Circle W has center W(−4, 6) and radius 10 units. Which point lies on circle W?
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Answer: J — (6, 16)
9. A transversal line ℓ intersects four lines labeled a, b, c, and d. At line a, the angle formed with ℓ is 75°. At line b, the angle formed with ℓ is 85°. At line c, the angle formed with ℓ is 105°. At line d, the angle formed with ℓ is 100°. Which two lines are parallel?
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Answer: A — a and c
10. Two parallel horizontal lines are cut by a transversal. At the upper intersection, angles are labeled 1 (upper left), 2 (upper right), 3 (lower left), and 4 (lower right). At the lower intersection, angles are labeled 5 (upper left), 6 (upper right), 7 (lower left), and 8 (lower right). ∠2 and ∠6 form which type of angle pair?
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Answer: J — corresponding angles
11. One exterior angle of a regular polygon measures 72°. What is the measure of one interior angle?
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Answer: B — 108°
12. Lines a and b are parallel, and lines c and d are parallel. A transversal intersects all four lines, creating 16 angles numbered sequentially from top to bottom and left to right. ∠1 is at the top intersection on line a. Which angle is not necessarily congruent to ∠1?
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Answer: H — ∠12
13. A bench leg makes a 130° angle with the ground. The seat of the bench must be parallel to the ground. What must be the measure of angle x, the angle between the leg and the seat?
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Answer: A — 50°
14. Line v is a transversal intersecting two lines, creating angles labeled w, x, y, and z. The measures shown are: one angle is 70°, another is 80°, another is 110°, and another is 100°, arranged so that w and x are adjacent on the upper line and y and z are adjacent on the lower line. Which statement is true?
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Answer: F — w ∥ y and x ∥ z
15. Lines ℓ and m are parallel and cut by a transversal. At the top intersection, angles are labeled 1–4; at the middle intersection, 5–8; at the bottom intersection, 9–16. ∠4 and ∠12 are —
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Answer: C — corresponding angles
16. A board is nailed across two beams, forming eight angles labeled 1 through 8. Which equality of angle measures would ensure the beams are parallel?
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Answer: G — m∠1 = m∠3
17. Points C, A, B, K, L, M, N, and R lie on several connected segments forming a figure. Segment AB is shown. Which segment is congruent to AB?
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Answer: D — CN
18. A point A is not on line ℓ. Points W, X, Y, and Z are shown near line ℓ. Which point lies on the perpendicular to line ℓ drawn from point A?
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Answer: F — X
19. A circular pie has center C. Points W, X, Y, and Z are on the circumference. Where should the pie be cut so that two boys receive equal shares?
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Answer: C — CX
20. If p → q and q → r, then —
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Answer: G — p → r
21. The conditional statement “If you have a laptop, then you have a computer” is represented by p → q. What is the symbolic representation of “If you have a computer, then you do not have a laptop”?
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Answer: A — q → ¬p
22. V represents the set of all vehicles. M represents the set of all motorized vehicles. A represents the set of all automobiles. A is entirely inside M, and M is entirely inside V. Which conclusion is valid?
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Answer: F — All automobiles are motorized vehicles.
23. Triangles IJK and LMN are shown with IJ = LM = 12 and IK = LN = 8. Which additional information would prove that △IJK ∼ △LMN?
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Answer: F — NM = 18
24. Given: M is the midpoint of LN and KP. Which postulate or theorem is sufficient to prove △KML ≅ △PMN?
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Answer: C — Side-Angle-Side
25. Which of the following could not be the lengths of the sides of a triangle?
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Answer: F — 6 ft, 3 ft, 9 ft
26. In △DEF, DE = 8 in., EF = 6 in., and DF = 10 in. Which lists the angles in order from smallest to largest?
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Answer: D — ∠D, ∠F, ∠E
27. In △ABC, if m∠C < m∠B < m∠A, then —
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Answer: F — AB < AC < BC
28. A finish-line banner forms a right triangle with the ground. One side is 7 ft, another is 8 ft, and the support rope is the hypotenuse labeled x. Which is closest to the length of the support rope?
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Answer: B — 10.6 ft
29. A baseball diamond is a square with side length 90 ft. What is the distance from home plate to second base?
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Answer: G — 90√2 ft
30. What is the length of a diagonal brace for a wall 9 ft high and 12 ft long?
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Answer: D — 15 ft
31. A parallelogram-shaped corral ABCD is adjacent to a shed. Angle at A is 40°. A gate CF swings from position CF to CG along the fence. Through how many degrees does the gate swing?
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Answer: H — 130°
32. A diagonal of parallelogram DEFG forms two adjacent angles measuring 56° and 44° at vertex E. What is m∠DEF?
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Answer: C — 80°
33. Quadrilateral MNOP is a parallelogram. M(1, 5), N(2, 1), O(−3, −2). If P has coordinates (x, 2), what is x?
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Answer: G — −4
34. Rectangular flowerbeds surround a fishpond shaped as a regular octagon. What is the measure of the angle between two consecutive flowerbeds?
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Answer: B — 45°
35. A portion of a regular polygon is shown with each exterior angle measuring 24°. How many sides does the polygon have?
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Answer: F — 15
36. Each interior angle of a regular polygon measures 162°. How many sides does the polygon have?
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Answer: D — 20
37. In circle O, the measure of arc PSR is 280°. What is the measure of central angle ∠POR?
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Answer: H — 80°
38. In trapezoid ABCD, bases AB and DC are parallel. AB = 26, DC = 40, one leg is 20, and the other leg is 2x + 6. What is the value of x?
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Answer: D — 7
39. In circle C, arc WX = 25°, arc XY = 40°, arc YZ = 25°, and chord WY = 24 cm. What is the length of chord XZ?
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Answer: G — 24 cm
40. A pizza has a diameter of 16 inches and is divided into 6 equal slices. Which is closest to the area of one slice?
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Answer: D — 33.5 sq in.
41. A solid is constructed from 1×1×1 cubes and is completely solid. What is the volume of the solid?
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Answer: G — 34 cubic units
42. Which is closest to the volume of a sphere with radius 8 cm?
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Answer: J — 2,143.6 cm³
43. What is the total surface area of a rectangular prism measuring 5 ft by 1 ft by 1 ft?
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Answer: C — 22 sq ft
44. Points P and Q are on one side of a lake, and points S and T are on the opposite side. PQ ∥ ST. Distances given are PQ = 30 m, PR = 28 m, and RT = 105 m. What is ST, the width of the lake?
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Answer: J — 98 m
45. The ratio of the perimeter of triangle U to triangle V is 1:2. The corresponding side lengths are labeled x, y, 2, 4, 5, and z. If the triangles are similar, what is x + y?
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Answer: C — 12
46. Right triangle ABC has side lengths 3, 4, and 5. What is the maximum number of lines of symmetry that can be drawn?
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Answer: F — 0
47. On a coordinate grid, point Q is at (−1, 2) and point V is at (1, −2). What is the slope of line QV?
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Answer: B — −1/2
48. One figure is mapped onto another by rotating all points 180° about the origin. Which transformation describes this?
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Answer: J — 180° rotation about the origin
49. Triangle ABC has vertices A(4, 5), B(5, 4), and C(1, 1). What is the midpoint of AB?
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Answer: C — (4.5, 4.5)
50. Rectangle ABCD has vertices A(2, 7), B(6, 7), C(6, 3), and D(2, 3). Which equation describes a line of symmetry?
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Answer: H — y = 5
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.