Geometry is one of the major topics you’ll need to know for the GED Mathematical Reasoning subject test. One of the best ways to prepare is simply to practice! Try your hand at these GED geometry sample problems. Answers and explanations are at the end of the post.
GED Geometry Sample Problems
1. Which choice shows an acute angle?
2. Which choice describes the triangle below?
3. What is the correct classification of the quadrilateral shown below?
4. Theo has a leaning bookcase in his living room. The bottom of the shelf rests 15 inches away from the wall. The top of the shelf rests against the wall, 75 inches up from the floor. Approximately how long is the shelf?
A. 73.48 inches
B. 76.49 inches
C. 80 inches
D. 90 inches
5. Theo draws up a floor plan of his living room space, shown below. He would like to add crown molding to connect the walls and ceiling all the way around the room. How many linear feet of crown molding does he need to complete this project?
6. Find the measure of angle x.
7. Which choice describes the triangle below?
A. acute isosceles
B. acute scalene
C. obtuse scalene
D. obtuse isosceles
8. Which word does NOT describe the figure below?
9. What is the area of the figure shown below?
A. 26 square meters
B. 48 square meters
C. 56 square meters
D. 50 square meters
10. One angle of a right triangle measures 50°. What is the measure of the smallest angle in the triangle?
A. 40 degrees
B. 50 degrees
C. 60 degrees
D. 70 degrees
An acute angle is one that is less than 90 degrees, or smaller than a right angle. Angle ABC is an obtuse angle, since it is greater than 90 degrees. Angle DEF is a right angle, which means it is exactly 90 degrees. Angle JKL is a 180-degree angle, which forms a straight line.
An equilateral triangle has three congruent side lengths. No other type of triangle matches this description. A scalene triangle has 3 different side lengths. A right triangle is a triangle with a 90-degree angle, regardless of the length of its sides. An isosceles triangle is a triangle with 2 equal side lengths.
A rhombus is a parallelogram with 4 equal side lengths, with opposite pairs of congruent obtuse and acute angles. Since this parallelogram has an opposite pair of congruent obtuse angles, you know it is a rhombus. A square also has 4 equal side lengths, but its 4 angles are each 90°. Rectangles also have four 90° angles and two pairs of opposite congruent sides. Trapezoids do not have four equal side lengths.
The bookcase, floor, and wall form a right triangle. The bookcase leaning against the wall represents the hypotenuse of the triangle. Thus, you can use the Pythagorean Theorem to solve:
a2 + b2= c2
152 + 752= c2
225 + 5625= c2
Since the length of the bookcase forms the hypotenuse of the triangle, the bookcase is 76.49 inches long.
To find the amount of crown molding needed, what you need to solve for is the perimeter of the figure (the distance all the way around the sides). To find the perimeter, you need to add up all the side lengths of the figure. The floor plan shown is missing some dimensions, but you can figure them out by drawing in some lines to create more familiar shapes inside the larger shape. If you divide the figure up as shown below, it is actually composed of two squares and a rectangle. While not all of the side lengths are given, you can find them all by remembering that opposite sides of both rectangles and square are of equal length:
Now, you just need to add up all of the wall lengths:
So Theo will need 48 linear feet of crown molding to trim all the walls of his living room.
Angles ABD and DBC are supplementary, since together they create a straight line, which is a 180-degree angle. This means that together their measurements will add up to 180 degrees. Since you know that the measure of angle DBC is 120 degrees, subtract 120 from 180 to find the other angle measure:
So, angle ABD is 60°.
Triangles can be classified by side lengths:
- Equilateral triangle- 3 equal sides
- Isosceles triangle- 2 equal sides
- Scalene triangle- no equal sides
and by angle measures:
- Acute triangle- 3 acute angles
- Right triangle- 1 right angle and 2 acute angles
- Obtuse triangle- 1 obtuse angle and 2 acute angles
The triangle shown has no equal sides and contains one obtuse angle. It is classified as an obtuse scalene triangle.
The figure is a quadrilateral because it has 4 sides. It is a parallelogram because each side is parallel with the side opposite. It is a rectangle because it has 4 right angles and two pairs of equal sides. It is not a square because a square has 4 equal side lengths.
The easiest way to approach this problem is to divide the figure up into two more familiar shapes. The composite figure consists of a square and a triangle. You know that the sides of the square have a length of 6 m. Use this to find the area. To find the area of a square, you simply square one side length:
So, the area of the square is 36 square meters
To find the area of the triangle, you need to know the base and the height. This missing side length of the square forms the base of the triangle, so you know that the base is 6 meters long. Since the height of the entire figure is 10 meters, to find the height of the triangle, you need to subtract the height of the square from 10:
So, the height of the triangle is 4 meters. You can now find the area of the triangle:
So, the area of the triangle is 12 square meters.
To find the area of the entire figure, add together the area of the square and the area of the triangle:
So, the area of the composite shape is 48 square meters.
A triangle has a total of 180 degrees. To find the measurement of the missing angle, you need to subtract the other two angles from 180. You already know that one angle is 50°. You also know that since this is a right triangle, another angle must measure 90°. First, subtract 90 from 180:
The other given angle is 50 degrees. So now, subtract 50 from 90:
So, the measure of the missing angle is 40°.
Need to study a little more?
Check out these resources:
- What’s on the GED Math Test?
- GED Geometry Formulas
- Geometry Word Problems
- Converting Units of Measurement