Geometry SOL Practice Test — Set 6 of 6
Set 6 of 6 — 50 more free Geometry SOL practice questions from official VDOE released tests.
1. Which Venn diagram accurately represents the information in the following statement? If a triangle is equilateral, then it is isosceles.
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Answer: A — All equilateral triangles are inside the set of isosceles triangles, which are inside the set of triangles.
2. Let ( p ) represent: Brent works this summer. Let ( q ) represent: Brent takes a vacation. Symbolically represent the following argument. If Brent works this summer, then he will not take a vacation. Brent takes a vacation. Therefore, Brent does not work this summer.
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Answer: B — ( p q, q, p )
3. Which type of construction is illustrated? The construction shows an angle with an arc intersecting both sides, followed by an arc from one intersection crossing the other side of the angle.
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Answer: B — An angle congruent to a given angle
4. Given statements: If a shape is a parallelogram, then opposite angles are congruent. A rhombus is a parallelogram. Which is a logical conclusion from the given statements?
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Answer: A — A rhombus has opposite angles that are congruent.
5. Which is the converse of the following statement? If ( b = c ), then ( a = bc ).
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Answer: B — If ( a = bc ), then ( c = b ).
6. Which statement describes the construction illustrated on the rectangle?
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Answer: D — A perpendicular to ( AB ) through point ( G ) not on ( AB )
7. Four lines and four congruent angles are identified. Which statement must be true?
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Answer: A — Only ( m n )
8. Triangle ( ABC ) is reflected across the x-axis and then across the y-axis to create triangle ( A'B'C' ). If point ( A ) is at ( (1, -4) ), what are the coordinates of ( A' )?
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Answer: C — ( (-1, -4) )
9. The coordinate values of the vertices of triangle ( KLM ) are integers. Which set of coordinate pairs could represent the vertices of a triangle congruent to ( KLM )?
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Answer: C — ( (-1,1), (-1,4), (2,1) )
10. The diagonals of a square measure 14 cm. Which is the length of a side of the square?
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Answer: A — ( 7sqrt2 ) cm
11. A right triangle has legs measuring 7.8 and 8. Which angle measure is closest to the value of ( x )?
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Answer: C — ( 45.7^ )
12. Two swimmers start at the same dock and swim in different directions. One swims 42 yards, the other 63 yards. Let ( d ) be the distance between them. Which represents all possible values of ( d )?
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Answer: C — ( 21 < d < 147 )
13. Given isosceles triangles ( LMN ) and ( PQR ) with vertex angles ( (2x-26)^ ) and ( (x+16)^ ), what value of ( P ) could be used to prove the triangles are congruent?
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Answer: C — ( 61^ )
14. Triangle ( LN ) is similar to triangle ( POR ). If triangle ( POR ) has side lengths 3 cm, 4 cm, and 5 cm, which set of side lengths could represent triangle ( LN )?
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Answer: D — 9 m, 12 m, 15 m
15. A convex polygon has vertices ( A, B, C, D, ) and ( E ). What is the sum of the measures of the interior angles of this polygon?
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Answer: B — ( 540^ )
16. The equation ( (x-1)^2 + (y-3)^2 = r^2 ) represents circle ( A ). Point ( B(4,7) ) lies on the circle. What is ( r )?
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Answer: B — 5
17. A circular garden sector has a radius of 13 ft and a central angle of ( 40^ ). Which is closest to the area of this section?
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Answer: A — 118 sq ft
18. The height of a cylinder is 9.5 cm. The diameter is 1.5 cm longer than the height. Which is closest to the volume of the cylinder?
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Answer: B — 287 cm³
19. Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each other?
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Answer: C — Rhombus
20. In a quilt pattern, angle measures are given: ( ABC = 120^ ) ( ADC = (2x+30)^ ) ( BCD = x^ ) What is the measure of ( DCE )?
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Answer: B — ( 140^ )
21. A rectangular prism has dimensions 18 in, 12 in, and 24 in. What is the surface area of the prism?
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Answer: C — 1,872 sq in
22. The volumes of two spheres are in a ratio of 1:8. What is the ratio of their radii?
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Answer: D — 1:2
23. The minute hand of a clock is 10 cm long and moves through an arc of ( 108^ ). Which is closest to the length of the arc?
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Answer: D — 18.8 cm
24. Which point lies on the circle represented by ( (x-1)^2 + (y-3)^2 = 7^2 )?
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Answer: D — ( (8,3) )
25. Consider the following statement. If (4x = 8), then (x = 2). Which is the inverse of the statement?
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Answer: D — If (4x = 8), then (x 2).
26. John wants to make a triangular garden. Which of the following are possible dimensions?
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Answer: H — 6 ft by 8 ft by 10 ft
27. Which of the following quadrilaterals is not a parallelogram?
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Answer: J — Trapezoid
28. When tiles are tessellated in a plane, what angle measure sum is required of the tiles surrounding a single point?
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Answer: C — 360°
29. The radius of Sphere A is 2 inches, and the radius of Sphere B is 4 inches. How many times larger is the volume of Sphere B compared to the volume of Sphere A?
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Answer: D — 8
30. A cylinder has a diameter of 10 inches and a height four times its radius. What is its volume?
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Answer: H — (4,000 ) cubic inches
31. Points (P(-3,5)), (Q(1,7)), (R(8,1)), and (S(-4,-5)) are connected to form a trapezoid. What is the midpoint of segment (SR)?
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Answer: B — ((4,-1))
32. A trapezoid is located entirely in Quadrant II. If this trapezoid is reflected across the x-axis, in which quadrant will the new trapezoid be located?
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Answer: H — III
33. A bisector of segment AB is a line that passes through the midpoint of AB and divides it into two congruent segments. Which line segment lies on the bisector of AB?
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Answer: D — EF
34. Lines m and r are cut by a transversal. The angle formed at the intersection with line m measures (3x − 35)°, and the corresponding interior angle formed at the intersection with line r measures (7x − 115)°. What value of x will show that line m is parallel to line r?
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Answer: F — 20
35. Lines a and b are parallel. A transversal intersects line a forming an interior angle of 120°, and intersects line b forming an angle labeled x°. The angle adjacent to x° on line b is 115°. What is the value of x?
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Answer: D — 60
36. Angle PQR has vertex Q. Points W, X, Y, and Z are located inside the angle. The bisector of ∠PQR divides the angle into two congruent angles. Which point lies on the bisector of ∠PQR?
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Answer: H — Y
37. In the figure, lines AB and DC intersect at point E. Angle AED measures 85°, and angle AEB measures 26°. For what measure of ∠D is AB parallel to DC?
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Answer: C — 69°
38. Two congruent triangles are shown. In triangle ABC, segment BC is marked congruent to a segment in triangle PQRST. Which line segment is congruent to BC?
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Answer: G — PR
39. Line q is a transversal of four parallel lines l, m, n, and p. At the intersection of q and line m, an angle measures 30°. At the intersection of q and line l, the corresponding angle is labeled x°. At the intersection of q and line n, the corresponding angle is labeled y°. What are the values of x and y?
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Answer: B — x = 30, y = 150
40. Parallel lines j and k are cut by transversal m. At the intersection with line j, an acute angle measures 32°. Angle 1 is the obtuse angle formed at the intersection of transversal m with line k on the interior side. What is m∠1?
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Answer: F — 32°
41. Lines y and z are cut by a transversal. On line y, the interior angle is 77°. On line z, the corresponding interior angle is labeled x°. For what value of x are y and z parallel?
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Answer: B — 77
42. Two angles form a linear pair. m∠1 = (15x − 5)° and m∠2 = (10x + 35)°. What is m∠1?
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Answer: J — 115°
43. Line segments painted on a parking lot form parallel parking spaces. One angle measures 118°, the angle adjacent to it on the same transversal is labeled w°, and the corresponding angle on the parallel line is labeled x°. Which equation can be used to show that these line segments are parallel?
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Answer: D — w + 118 = 180
44. Given: △ABC ∼ △LMN. In △ABC, AB = 5x + 5, BC = x + 4, and AC = 10. In △LMN, LM = 3x + 3, MN = 3x + 1, and LN corresponds to AC. What is the length of AC?
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Answer: G — 12
45. Given the following measures of the sides of triangles, which is a right triangle?
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Answer: A — 41 cm, 40 cm, 9 cm
46. A Venn diagram shows rectangles and rhombi as subsets within quadrilaterals, with rectangles and rhombi overlapping. Which statement must be true about this diagram?
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Answer: G — Some rhombi are rectangles.
47. In a quadrilateral, diagonals AC and BD intersect at point E and bisect each other. Based on this information, which triangle congruence theorem could be used to prove △AED ≅ △CEB?
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Answer: C — Side-Angle-Side (SAS)
48. Statement: If lines are skew, then they are not coplanar. What is the contrapositive of the statement?
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Answer: H — If lines are coplanar, then they are not skew.
49. Coordinates A(2, 5), B(6, 4), and C(6, 0) form △ABC. If △CDA is congruent to △ABC, what are the coordinates of point D?
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Answer: D — (2, 1)
50. Let p = “An equation is of the form y = mx + b.” Let q = “Its graph is a line.” Argument: If an equation is of the form y = mx + b, then its graph is a line. The graph is not a line. Therefore, the equation is not of the form y = mx + b. Which is the symbolic representation of the argument?
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Answer: F — p → q, ∼q, therefore ∼p
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.