# 8th Grade Math : Geometry

## Example Questions

### Example Question #1 : Geometry

The image provided contains a set of parallel lines,  and , and a transversal line, . If angle  is equal to , then which of the other angles is equal to

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other.

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships.

Angle  and  are vertical angles.

Angle  and  are corresponding angles.

Angle  and  are exterior angles.

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are vertical angles; thus, both angle  and  are congruent and equal

### Example Question #2 : Geometry

Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.

Explanation:

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle."

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

### Example Question #3 : Geometry

Calculate the volume of the cone provided. Round the answer to the nearest hundredth.