Geometry SOL Practice Test — Set 1 of 6
347 free Geometry Virginia SOL practice questions drawn from official Virginia Department of Education released tests. Pick an answer to check it instantly, or open “Show answer” to review. No signup required.
1. If △ABC is similar to △ADE, then AB : AD =? : AE. Which replaces “?” to make the statement true?
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Answer: C — DE
2. George used decorative fencing to enclose his deck. Using the information below and assuming the top and bottom sides are parallel: A quadrilateral has one interior angle labeled x. Adjacent interior angles along one transversal are 130° and 50°. The top and bottom sides are parallel. What is the measure of ∠x?
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Answer: F — 50°
3. Angle 1 is a complement of angle 2. If m∠1 = (14x − 8) and m∠2 = (8x + 6), what is the value of x and of m∠1?
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Answer: B — x = 4, m∠1 = 64°
4. In a figure, two parallel lines l and m are cut by a transversal t. Eight angles are formed and labeled 1 through 8 in standard order. Which pair of angles are alternate interior angles?
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Answer: H — ∠4 and ∠5
5. Lines BA and CD are intersected by a transversal, forming four angles labeled 1 through 4 at the top intersection and four angles labeled 5 through 8 at the bottom intersection. BA is parallel to CD if which condition is true?
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Answer: H — m∠1 + m∠2 = 90
6. In triangle XYZ, the measure of ∠YZV is 40° and the measure of ∠XYZ is 65°. Which of these angles must measure 40° in order for VR to be parallel to YZ?
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Answer: B — ∠ZVR
7. Lines l and m contain the points shown below: Line l passes through (−3, 3) and (6, 0). Line m passes through (−5, 1). Which of the following points must lie on line m in order for lines l and m to be parallel?
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Answer: H — (1, −1)
8. Segment AB is horizontal. Point P lies above AB. Which point lies on the line through P perpendicular to AB?
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Answer: A — Q
9. Points A and B form a line segment. Points X, Y, Z, and W are arranged so that X and Z are directly above and below the midpoint of AB. Which pair of points determines the perpendicular bisector of line segment AB?
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Answer: G — X and Z
10. Which of the following groups of statements represents a valid argument?
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Answer: H — Given: All parallelograms have four sides. Conclusion: All parallelograms are quadrilaterals.
11. Which is the contrapositive of the statement, “If I am in Richmond, then I am in Virginia”?
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Answer: C — If I am not in Virginia, then I am not in Richmond.
12. A surveyor measured along a river and formed a triangle with sides 40 ft, 80 ft, and 120 ft. What is the distance across the river from point A to point T?
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Answer: F — 60 ft
13. From shortest to longest, the sides of △ABC are ordered based on opposite angle measures of 59°, 57°, and 64°. Which ordering is correct?
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Answer: D — AB, AC, BC
14. In a triangle, m∠C = 125° and m∠B = 35°. Which is the shortest side of the triangle?
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Answer: J — BC
15. On a map, Tannersville, Chadwick, and Barkersville form a triangle. Chadwick is 70 miles from Tannersville, and Barkersville is 90 miles from Tannersville. Which is a possible distance between Chadwick and Barkersville?
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Answer: C — 150 miles
16. A circular design shows a 30° central angle and a chord length of 5 cm opposite that angle. How long is the radius of the circle?
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Answer: F — 10 cm
17. A carpenter builds stairs that form a 30° angle with the floor. The vertical rise is 10 ft. What is the horizontal distance from the foot of the stairs to the wall?
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Answer: B — 17.3 ft
18. The lengths of two consecutive sides of a parallelogram are 10 inches and 15 inches, and the included angle is 60°. To the nearest tenth of a square inch, what is the area of the parallelogram?
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Answer: G — 129.9 sq in.
19. In quadrilateral KLMN, the interior angles are labeled 3x°, (x + 25)°, 95°, and 80°. What is the value of x?
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Answer: B — 40
20. Three vertices of a parallelogram have coordinates (0, 1), (3, 7), and (4, 4). What are the coordinates of the fourth-quadrant vertex?
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Answer: G — (1, −2)
21. Figure ABCDEF is a regular hexagon. Point Q lies at the center of the hexagon. What is the measure of ∠CDQ?
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Answer: B — 60°
22. In pentagon ABCDE, m∠E = m∠C and m∠D = m∠B. The measures of ∠B and ∠C are given as 100° and 105°. What is the measure of ∠A?
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Answer: J — 130°
23. Three adjacent angles around point B measure (19x − 15)°, (26x + 20)°, and (9x + 25)°. What is the measure of ∠ABD?
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Answer: A — 150°
24. Triangle ABC is circumscribed about circle O. Points P and Q are points of tangency. BP = 3 and CQ = 5. What is the measure of BC?
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Answer: J — 8
25. In a circle, m∠CAB = 40°. What is m∠CDB?
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Answer: B — 40°
26. AB is tangent to circle C at B. AB = 15 cm, and the radius of the circle is 8 cm. To the nearest tenth of a centimeter, what is the length of AC?
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Answer: H — 17.0 cm
27. A stained-glass window is in the shape of a semicircle with a radius of 8 ft. Ignoring seams, how much glass is needed?
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Answer: B — 8π sq ft
28. The cargo space of a truck is 2.44 m wide, 2.76 m high, and 8.20 m long. How many cubic meters of cargo space does the truck have?
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Answer: B — 55.22
29. What is the approximate volume of a can that is 5 inches tall and has a 2.5-inch diameter?
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Answer: G — 24.5 cu in.
30. A rectangular prism tank measures 40 cm by 20 cm. The water level rises 0.4 cm when a rock is submerged. What is the volume of the rock?
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Answer: A — 320 cm³
31. The ratio between the volumes of two spheres is 27 to 8. What is the ratio between their radii?
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Answer: J — 3:2
32. A surveyor measures distances of 12 ft and 9 ft along one bank of a river and 52 ft along the opposite bank. Which is a good estimate of the distance across the river?
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Answer: C — 40 ft
33. All vertices of a hexagon have integer coordinates. One line of symmetry passes through which two points?
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Answer: F — (−4, 3) and (4, 3)
34. Polygon A′B′C′D′E′ is obtained from polygon ABCDE by reflecting each point across the x-axis. Which transformation describes this change?
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Answer: D — Reflection across the x-axis
35. The midpoint of segment AB is (−2, 1). The coordinates of A are (2, 3). What are the coordinates of B?
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Answer: D — (−6, −1)
36. An airplane travels due north at 300 knots. The wind blows from the east at 50 knots. Which is closest to the resultant speed of the airplane?
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Answer: B — 304 knots
37. Which value for x is a counterexample to the following statement? For all positive values of x, x² > x.
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Answer: B — −0.1
38. The following information describes a Venn diagram showing lunch selections made by athletes. • A total of 310 athletes selected a sandwich. • A total of 125 athletes selected both a sandwich and a salad. • A total of 180 athletes selected both a sandwich and a soup. • The total number of athletes who selected a sandwich includes those who may also have selected salad, soup, or both. How many athletes selected a sandwich, a soup, and a salad?
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Answer: H — 65
39. The following information represents a Venn diagram of triangles. • One circle represents Acute Triangles. • One circle represents Isosceles Triangles. • The two circles overlap. Which statement is valid?
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Answer: D — Some triangles are both acute and isosceles.
40. Lines j and k are cut by transversals m and n. Three angles are formed with the following measures: • One angle measures (x + y)°. • A corresponding angle on the same transversal measures (x + 30)°. • Another angle formed by the second transversal measures (3x − y − 60)°. Which relationship is sufficient to prove that j ∥ k?
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Answer: C — y = x − 30
41. The perimeter of triangle JKL is 200 centimeters. • JK = 68 centimeters • KL = 62 centimeters Which statement is true about the interior angles of triangle JKL?
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Answer: H — m∠K is the greatest of the interior angles
42. Two triangles, △STW and △XYZ, are shown with corresponding side lengths expressed in terms of x. For △STW, the side lengths are: • ST = x + 5 • TW = 3x + 1 • SW = 3x − 1 For △XYZ, the corresponding side lengths are: • XY = 4x − 3 • YZ = 4x − 5 • XZ = 2x + 1 Which value of x makes △STW ≅ △XYZ?
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Answer: A — 2
43. The figure is a regular hexagon with each side measuring 4 inches. Points A, B, C, D, E, and F label consecutive vertices of the hexagon. What is the length of diagonal AC?
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Answer: A — 4√3 in.
44. A shed is modeled as a combination of a triangular prism and a rectangular prism. A vertical plane intersects the model and is parallel to the front face of the shed. What is the shape of this cross section?
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Answer: H — Rectangle
45. Using the same shed model, the following dimensions are given: • w = 12 feet • h = 6 feet What is the surface area of the exterior walls and doors of the shed?
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Answer: C — 468 square feet
46. Using the same shed model, if w = 12 feet, which equation correctly models the volume of the shed?
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Answer: J — V = 18(12)(h) + ½(18)(12)(9 − h)
47. A cylinder has a volume of 300π cubic centimeters and a base with a circumference of 10π centimeters. What is the height of the cylinder?
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Answer: C — 12 cm
48. The height of a rectangular prism is decreased by a factor of 1/4. The other dimensions are unchanged. Which statement is true?
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Answer: F — The volume is decreased by a factor of 1/4.
49. A company makes two similar cylindrical containers. The total surface area of the smaller container is 0.81 times that of the larger container. The height of the larger container is 60 centimeters. What is the height of the smaller container?
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Answer: B — 48.6 cm
50. Given quadrilateral ABCD with coordinates: A(0, 0), B(r, 0), C(r, m), D(0, m) Which expression proves that ABCD is a rectangle?
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Answer: F — The length of each diagonal is √(r² + m²).
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.