Geometry Practice Problems for McGraw-Hill's ASVAB

The study guide for this quiz can be found at:

Geometry Study Guide for McGraw-Hill's ASVAB

1. The endpoint shared by two rays that form an angle is called a
   1. line segment.
   2. degree.
   3. vertex.
   4. straight line.
2. A right angle is an angle that measures
   1. exactly 90°.
   2. greater than 90°.
   3. less than 90°.
   4. 45°.
3. An acute angle is an angle that measures
   1. exactly 90°.
   2. greater than 90°.
   3. less than 90°.
   4. exactly 180°.
4. An obtuse angle is an angle that measures
   1. exactly 90°.
   2. between 90° and 180°.
   3. exactly 180°.
   4. greater than 180°.
5. In the figure shown, if angle 1 measures 65°, what is the measure of angle 2?

   

   1. 120°
   2. 90°
   3. 25°
   4. 10°
6. In the figure shown, if angle 1 measures 35°, what is the measure of angle 2?



1. 145°
2. 95°
3. 65°
4. 45°
7. In the figure shown, if angle 2 measures 45°, what is the measure of angle 4?



1. 135°
2. 75°
3. 45°
4. 35°
8. In the figure shown, lines AB and CD are parallel and angle 1 measures 120°. What is the measure of angle 2?



1. 60°
2. 90°
3. 120°
4. 180°
9. A certain triangle has exactly two equal sides, and the angles opposite those sides are also equal. This triangle is a(n)
   1. isosceles triangle.
   2. scalene triangle.
   3. equilateral triangle.
   4. right triangle.
10. In the equilateral triangle shown, what is the measure of each angle?



1. 60°
2. 90°
3. 120°
4. 180°
11. In the triangle shown, ACB measures 55° and CAB measures 65°. What is the measure of CBA?



1. 50°
2. 60°
3. 80°
4. 90°
12. In the triangle shown, side a is 5 in. long and side b is 6 in. long. How long is side c?



1. 7.81 in.
2. 8.51 in.
3. 9.11 in.
4. 10.71 in.
13. In the rectangle shown, side a measures 13 cm and side b measures 36 cm. What is the perimeter of the rectangle?



1. 49 cm
2. 98 cm
3. 469 cm
4. 512 cm
14. In the triangle shown, side a is 4 ft long, side b is 6 ft long, and side c is 8 ft long. What is the area of the triangle?



1. 12 ft²
2. 12 ft²
3. 18 ft²
4. 24 ft²
15. In which of the following circles is the line segment a diameter?
    1. 
    2. 
    3. 
    4. 
16. The circle shown has a diameter of 12 m. What is the area of the circle?



1. 452.16 m²
2. 360 m²
3. 144 m²
4. 113.04 m²
17. In the trapezoid shown, b₁ = 4 ft, b₂ = 8 ft, and h = 5 ft. What is the area of the trapezoid?



1. 16 ft²
2. 30 ft²
3. 90 ft²
4. 160 ft²
18. Figure WXYZ is a parallelogram. Which of the following is NOT necessarily true?



1. Side WX is parallel to side ZY.
2. Side XY is parallel to side WZ.
3. W has the same measure as Y.
4. Side WX is the same length as side XY.
19. Which of the following figures contains line segments that are perpendicular?
    1. 
    2. 
    3. 
    4. 
20. What is the ratio of the length of a side of an equilateral triangle to the triangle's perimeter?
    1. 1:1
    2. 1:2
    3. 1:3
    4. 3:1
21. Jules needs to purchase a ladder that just reaches the top of a 16-foot building. If the bottom of the ladder will be placed 12 feet from the base of the building, how long should Jules's ladder be?
    1. 18 ft
    2. 20 ft
    3. 25 ft
    4. 30 ft
22. Kai must buy canvas to make a sail for his sailboat. The sail will have the shape of a right triangle. It will be as tall as the mast (the vertical pole) and as wide at the bottom as the boom (the horizontal pole). If the mast measures 18 meters and the boom measures 9 meters, about how much canvas does Kai need to buy?
    1. 27 m²
    2. 61 m²
    3. 81 m²
    4. 103 m²
23. Renee wants to carpet her living room. If the room measures 15 feet × 18 feet, how many square yards of carpet must she purchase?
    1. 20 yd²
    2. 30 yd²
    3. 32 yd²
    4. 35 yd²
24. Saul wants to wallpaper one wall in his dining room. The wall is 11 ft high and 14 ft long. It has a window that measures 3 ft by 4 ft. About how many square feet of wallpaper must Saul buy?
    1. 25 ft²
    2. 32 ft²
    3. 112 ft²
    4. 142 ft²
25. In the following figure, line AB intersects two parallel lines. If angle 1 measures 35°, what is the measure of angle 4?



1. 35°
2. 55°
3. 90°
4. 145°
26. The Lakeville skating rink is a perfect circle. If the diameter of the rink is 50 ft, which of the following best represents its area? (Use π = 3.14)
    1. 78.5 ft²
    2. 157 ft²
    3. 1,962 ft²
    4. 7,850 ft²
27. A tomato paste can has a diameter of 8 cm and a height of 20 cm. Which of the following tells about how much tomato paste it will hold?
    1. 4,019 cm³
    2. 1,005 cm³
    3. 201 cm³
    4. 50 cm³
28. In the figure shown, what is the area of the rectangle if the radius of each circle is 6 cm?



1. 72 cm²
2. 112 cm²
3. 288 cm²
4. 310 cm²
29. A square garden is doubled in length and 4 feet is added to its width. Which of the following expressions represents the new area of the garden?
    1. 2x(x + 4)
    2. 4x²
    3. 4x + 4
    4. (2x)(4x)
30. A rectangular garden is 40 yards long and 15 yards wide. Darryl runs once around the edge of the garden. How far does Darryl run?
    1. 55 yards
    2. 80 yards
    3. 100 yards
    4. 110 yards

Answers