Geometry SOL Practice Test — Set 5 of 6
Set 5 of 6 — 50 more free Geometry SOL practice questions from official VDOE released tests.
1. Which is the contrapositive of the statement: “If you do your homework, then you will be prepared for the test.”
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Answer: B — If you are not prepared for the test, then you did not do your homework.
2. If triangle XYZ is similar to triangle XLM, which proportion must be true?
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Answer: A — XM : XZ = XL : XY
3. Given ABCD is a parallelogram. Prove ΔABD ≅ ΔCDB. Opposite sides of a parallelogram are congruent, and opposite angles are congruent. Which postulate or theorem proves the triangles congruent?
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Answer: C — SAS
4. Three boys are flying kites at points J, K, and L. Viewed from above, ∠K = 45° and ∠J = 65°. Which angle has the least measure?
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Answer: D — All are equal
5. Which list orders the sides of triangle JKL from least to greatest?
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Answer: C — KJ, LK, JL
6. A fire truck has a ladder that can extend to 60 feet and can be raised to a maximum angle of 75° with the horizontal. Disregarding the height of the truck, which is closest to the maximum height the ladder can reach?
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Answer: B — 57.96 ft
7. Scotty is making a triangular arrangement of dominoes. The bottom row has 8 dominoes, the next row has 7, continuing upward by one fewer domino per row. How many dominoes are needed to complete the triangle?
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Answer: B — 36
8. The spokes on a wagon wheel form twelve congruent central angles. What is the measure of each central angle?
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Answer: A — 30°
9. XYZW is a rectangle. Which of the following is not necessarily true?
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Answer: D — ∠X = ∠Y
10. A regular polygon is partially covered by a rectangle. The uncovered interior angle shown measures 135°. What is the number of sides of the polygon?
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Answer: C — 8
11. If ∠E = ∠C in a circle with center O, and m∠AOB = 45°, what is the measure of the intercepted arc?
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Answer: C — 67.5°
12. Three vertices of a parallelogram are (1, −4), (3, 8), and (5, 0). What are the coordinates of the vertex in the second quadrant?
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Answer: B — (1, 4)
13. In rectangle PQRS, m∠1 = 50°. What is the measure of ∠2?
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Answer: B — 85°
14. A regular pentagon and a regular hexagon share a side. What is the measure of the angle formed between their non-shared sides at the shared vertex?
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Answer: C — 132°
15. The sum of the measures of arcs AB and BC is equal to which arc?
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Answer: A — arc AC
16. A swimming pool is 18 yards long, 10 yards wide, and 3 yards deep. Water is added at a rate of 12 cubic yards per minute. How many minutes will it take to fill the pool?
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Answer: A — 45
17. Cubic boxes are stacked in a corner in a 4 by 4 by 4 arrangement. Each box holds 8 cubic feet. What is the total capacity of the stack?
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Answer: B — 496 cubic feet
18. A machine produces cylindrical bales of hay with diameter 6 feet and height 5.5 feet. Which is closest to the volume of one bale?
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Answer: B — 151 cubic feet
19. A boy is 6 feet tall and casts a 4-foot shadow. At the same time, a tree casts a 24-foot shadow. What is the height of the tree?
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Answer: A — 36 ft
20. The cylinders shown are similar. The smaller cylinder has radius 2 m and height 7 m. The larger has radius 4 m. What is the volume of the larger cylinder?
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Answer: D — 3584π m³
21. If parallelogram ABCD is translated so that point D moves to (−1, 2), what is the new location of point B?
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Answer: B — (3, 4)
22. Triangle A′B′C′ is a transformation of triangle ABC such that A maps to A′, B to B′, and C to C′, reversing orientation across a line. What transformation occurred?
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Answer: A — Reflection
23. What is most likely the slope of the line graphed, which rises 2 units for every 1 unit it moves to the right?
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Answer: D — 2
24. The figure shown is symmetric with respect to which line(s)?
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Answer: C — both lines ℓ and m
25. What is the point of intersection of diagonals BD and AC of a square with vertices at (2,2), (4,2), (4,4), and (2,4)?
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Answer: A — (3, 3)
26. What is the midpoint of the segment joining (12, 2) and (−5, −7)?
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Answer: D — (3.5, −2.5)
27. Which is a valid conclusion that can be drawn from these statements? If a quadrilateral is a rhombus, then it is a parallelogram. If a quadrilateral is a parallelogram, then its opposite angles are congruent.
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Answer: C — Opposite angles of a rhombus are congruent.
28. Given points S(−1, 8) and T(7, −9), what is the length of segment ST?
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Answer: D — √353
29. Which is the inverse of the following statement? If the measure of an angle is 90°, then it is a right angle.
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Answer: A — If the measure of an angle is not 90°, then it is not a right angle.
30. Given points P(5, 7) and T(−3, 3), what is the slope of line PT?
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Answer: C — 1/2
31. Which of the following sets of lengths can represent the measures of the sides of a right triangle?
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Answer: D — 20, 21, 29
32. Part of a marching band formed a triangle with trumpet players on one side, clarinet players on one side, and flute players on the third side. The angle formed by the trumpet and flute players measures 45°. The angle formed by the flute and clarinet players measures 68°. Which orders the sides of this triangle from least to greatest using the instrument names?
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Answer: B — Clarinet, flute, trumpet
33. An equilateral triangle has side length 14 cm. The triangle is folded in half along an altitude. What is the height of the equilateral triangle?
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Answer: C — 7√3 cm
34. Which could be the lengths of three sides of a triangle?
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Answer: C — 8.5 cm, 17 cm, 10.6 cm
35. Given a circle with center at (−4, 1), which equation could represent the circle if its radius is √41?
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Answer: C — (x + 4)² + (y − 1)² = 41
36. Circle O has a center at (−2, −2) and a diameter of 10 units. Which point lies on circle O?
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Answer: B — (−2, 2)
37. An architect designs a curved balcony using a circle with radius 40 feet and a central angle of 70°. Which is closest to the length of railing needed for the curved section of the balcony?
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Answer: A — 24 ft
38. The volume of a cube is 64 cubic centimeters. What is the surface area of the cube?
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Answer: B — 96 cm²
39. The diagonals of rectangle KLMN intersect at the point (2, 1). One vertex of the rectangle is at (−4, 5). Which of the following could be the location of another vertex of this rectangle?
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Answer: A — (8, −3)
40. A company is creating a new cylindrical container to replace its original cylindrical container. The new container will have 4 times the volume of the original container. The height of the new container will remain the same. The length of the radius of the new container will be —
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Answer: A — 2 times the length of the radius of the original container
41. A guy wire for a pole for a tennis net makes an angle of 62° with the ground. What is the measure of the angle between the wire and the pole?
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Answer: A — 28°
42. Triangle ABC is a right triangle. One leg measures 7 inches, the other leg measures 24 inches, and the hypotenuse is unknown. What is the length of the hypotenuse BC?
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Answer: B — 24 in.
43. In triangle ABC, AC = 6, AB = 7, and BC = 5. Which is true?
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Answer: B — The measure of ∠C is the greatest of the three angles.
44. Triangle ABC has angles measuring 70° at A and 60° at B. Which of the following lists the sides of triangle ABC from least to greatest length?
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Answer: C — AB, AC, BC
45. ABCD is a rhombus. A(0,0), B(3,4), and D(5,0) are known vertices. What are the coordinates of vertex C?
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Answer: C — (8, 4)
46. A right circular cone is on top of a hemisphere with the same radius. The radius is 4 cm, and the height of the cone is 4 cm. To the nearest whole number, what is the volume of this solid?
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Answer: A — 201 cm³
47. A cylindrical water container is 1.2 meters high and has a diameter of 4.6 meters. Approximately how many cubic meters of water will the container hold when it is half full?
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Answer: B — 9.97
48. Which point is the greatest distance from the origin?
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Answer: A — (−8, −5)
49. The slope of the line joining the coordinate points (3, 1) and (−4, 7) is —
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Answer: A — −6/7
50. SAMPLE A For what value of ( x ) is triangle ( ABC ) similar to triangle ( DEF )?
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Answer: B — 21
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.