Alternate Interior Angles in Geometry

Understanding Alternate Interior Angles

Alternate interior angles are a type of angle found in geometry. Alternate interior angles are formed when two parallel lines are intersected by a third line. When two lines are parallel, it is said that the two lines remain the same distance apart, meaning that they never cross. When a third line, or transversal line, intersects the two parallel lines, it will create eight angles. Alternating interior angles are those that are located on opposite sides of the transversal line, yet still lie between the two parallel lines.

Alternate interior angles are always congruent, meaning that they have the same measure. This is because the angles are formed between the parallel lines and the transversal line. If the lines are parallel, then the angles formed by the transversal line will always be the same, regardless of the direction the transversal line is facing.

Alternate interior angles are also sometimes referred to as zig zag angles because they form a zig zag pattern when looking at the two lines that are parallel. This is because the angles alternate in direction, meaning that one angle is pointing up and one is pointing down.

Formulas for Alternate Interior Angles

There are two formulas for alternate interior angles. The first formula is:

Alternate Interior Angles = 180� - (Angle 1 + Angle 2)

The second formula is:

Alternate Interior Angles = 180� - (Angle 3 + Angle 4)

These formulas can be used to find the measure of alternate interior angles. To use the formula, you must first identify the angles that are given. Then, you must plug the angles into the formula to find the measure of the alternate interior angles. It is important to note that the angles must be in degrees when using the formula.

Examples of Alternate Interior Angles

Alternate interior angles can be seen in everyday life. For example, when two roads cross, the angle formed by the intersection of the two roads is an example of an alternate interior angle. Additionally, when two walls intersect, the angles formed by the intersection are also alternate interior angles. Alternate interior angles can be found in many different places.

Practice Problems

Now that we have a better understanding of alternate interior angles, let's practice some problems.

1. In the diagram below, find the measure of angle 3.

Answer: Angle 3 = 120�

2. In the diagram below, find the measure of angle 5.

Answer: Angle 5 = 60�

3. In the diagram below, find the measure of angle 7.

Answer: Angle 7 = 90�

4. In the diagram below, find the measure of angle 8.

Answer: Angle 8 = 30�

5. In the diagram below, find the measure of angle 9.

Answer: Angle 9 = 150�

6. In the diagram below, find the measure of angle 10.

Answer: Angle 10 = 120�

Summary

In this article, we discussed alternate interior angles in geometry. We discussed what alternate interior angles are and how to identify them. We also discussed the formulas for alternate interior angles and provided some examples of alternate interior angles in everyday life. Finally, we provided some practice problems to help you practice identifying alternate interior angles. Remember, alternate interior angles are always congruent and they form a zig zag pattern when looking at two parallel lines.

FAQ

What is example of alternate interior angles?

Alternate interior angles are two angles located on opposite sides of a transversal and inside the two lines it intersects. An example of this would be two angles located on opposite sides of a transversal and between two parallel lines.

What is alternate in geometry?

Alternate in geometry refers to two items that are located on opposite sides of a transversal, line, or plane. This can include angles, sides, and points.