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# Geometry Practice Problems for GED Math

By
Updated on Jan 17, 2011

Review these concepts if necessary:

### Problems

GEOMETRY IS THE STUDY of shapes and the relationships among them. The geometry that you are required to know for the GED Mathematics Exam is fundamental and practical. You should become familiar with the properties of angles, lines, polygons, triangles, and circles, as well as the formulas for area, volume, and perimeter. A grasp of coordinate geometry will also be important when you take the GED.

Use the following diagram to answer questions 1 to 5. The diagram is not to scale.

1. If the measure of angle 2 is equal to 12x + 10 and the measure of angle 8 is equal to 7x – 1, what is the measure of angle 2?
1. 9 degrees
2. 62 degrees
3. 108 degrees
4. 118 degrees
5. The measure cannot be determined.
2. If the measure of angle 5 is five times the measure of angle 6, what is the measure of angle 5?
1. 30 degrees
2. 36 degrees
3. 120 degrees
4. 130 degrees
5. 150 degrees
3. If the measure of angle 4 is 6x + 20 and the measure of angle 7 is 10x – 40, what is the measure of angle 6?
1. 60 degrees
2. 70 degrees
3. 110 degrees
4. 116 degrees
5. 120 degrees
4. Which of the following is NOT true if the measure of angle 3 is 90 degrees?
1. Angles 1 and 2 are complementary.
2. Angles 3 and 6 are supplementary.
3. Angles 5 and 7 are adjacent.
4. Angles 5 and 7 are congruent.
5. Angles 4 and 8 are supplementary and congruent.
5. If the measure of angle 2 is 8x + 10 and the measure of angle 6 is x2 – 38, what is the measure of angle 8?
1. 42 degrees
2. 74 degrees
3. 84 degrees
4. 108 degrees
5. 138 degrees
6. The length of a rectangle is four less than twice its width. If x is the width of the rectangle, what is the perimeter of the rectangle?
1. 2x2 – 4x
2. 3x – 4
3. 6x – 4
4. 6x + 4
5. 6x – 8
7. The area of one face of a cube is 9x square units. What is the volume of the cube?
1. 27 cubic units
2. 27x cubic units
3. 27x cubic units
4. 27x2 cubic units
5. 27x3 cubic units
8. If the diameter of a circle is doubled, the circumference of the new circle is
1. one-fourth of the circumference of the original circle.
2. one-half of the circumference of the original circle.
3. the same as the circumference of the original circle.
4. two times the circumference of the original circle.
5. four times the circumference of the original circle.
9. If the height of a triangle is half its base, b, what is the area of the triangle?
10. The bases of a right triangle measure x – 3 and x + 4. If the hypotenuse of the triangle is 2x – 3, what is the length of the hypotenuse?
1. 4
2. 5
3. 8
4. 12
5. 13
11. The endpoints of a line segment are (–3,6) and (7,4). What is the slope of this line?
1. –5
2. 5
3. 10
12. What is the midpoint of a line segment with endpoints at (0,–8) and (–8,0)?
1. (–8,–8)
2. (–4,–4)
3. (–1,–1)
4. (4,4)
5. (8,8)
13. What is the distance from the point (–6,2) to the point (2,17)?

Use the following diagram to answer questions 14 to 18.

Lines AE, BF, GD, and ray OC all intersect at point O (not labeled), and AE is perpendicular to OC.

1. Which of the following pairs of angles are complementary?
1. angles 1 and 2
2. angles 2 and 3
3. angles 1 and 4
4. angles 1, 2, and 3
5. angles 1, 6, and 7
2. Which of the following number sentences is NOT true?
1. angle 1 + angle 2 = angle 3 + angle 4
2. angle 1 + angle 2 + angle 3 + angle 7 = angle 4 + angle 5 + angle 6
3. angle 2 + angle 3 = angle 6
4. angle 1 + angle 7 = angle 2 + angle 3
5. angle 2 + angle 3 + angle 4 + angle 5 = 180 degrees
3. If the measure of angle 3 is 2x + 2 and the measure of angle 4 is 5x – 10, what is the measure of angle 7?
1. 14 degrees
2. 30 degrees
3. 60 degrees
4. 90 degrees
5. 115 degrees
4. If angle 1 measures 62 degrees and angle 4 measures 57 degrees, what is the measure of angle 6?
1. 33 degrees
2. 61 degrees
3. 72 degrees
4. 95 degrees
5. 119 degrees
5. If the measure of angle 3 is 5x + 3 and the measure of angle 4 is 15x + 7, what is the sum of angles 5 and 6?
1. 67 degrees
2. 113 degrees
3. 134 degrees
4. 157 degrees
5. The sum cannot be determined.
6. The length of a rectangle is 4 times the length of a square. If the rectangle and the square share a side, and the perimeter of the square is 2 units, what is the perimeter of the rectangle?
1. 5 units
2. 6 units
3. 8 units
4. 10 units
5. 20 units
7. The area of a rectangle is x2 + 7x + 10 square units. If the length of the rectangle is x + 2 units, what is the width of the rectangle?
1. x + 2 units
2. x + 4 units
3. x + 5 units
4. 2x + 4 units
5. x2 + 6x + 8 units
8. The length of a rectangular solid is twice the sum of the width and height of the rectangular solid. If the width is equal to the height and the volume of the solid is 108 cubic inches, what is the length of the solid?
1. 3 inches
2. 6 inches
3. 8 inches
4. 9 inches
5. 12 inches
9. If the length of the base of right triangle DEF is 8 units and the hypotenuse of DEF is 8 units, what is the length of the other base?
1. 4 units
2. 8 units
3. 8 units
4. 16 units
5. 32 units
10. If the measure of angle A of triangle ABC is 3x, the measure of angle B is 5x, and the measure of angle C is 4x, what is the value of x?
1. 12
2. 15
3. 20
4. 30
5. 45
11. What is the distance from the point (0,–4) to the point (4,4)?
1. 5 units
2. 4 units
3. 4 units
4. 4 units
5. 4 units
12. What is the midpoint of a line segment with endpoints at (6,–4) and (15,8)?
1. (9,4)
2. (9,12)
3. (10.5,2)
4. (12,2)
5. (12,9)
13. The endpoints of a line segment are (5,–5) and (–5,–5). What is the slope of this line?
1. –10
2. –5
3. 0
4. 5
5. This line has no slope.