Define Alternate Interior Angles
Alternate interior angles are a type of angle formed when two parallel lines are intersected by a transversal. These angles are located on opposite sides of the transversal and on the inside of the parallel lines. In this article, we will define alternate interior angles and explain how to calculate them.
Definition of Alternate Interior Angles
Alternate interior angles are a pair of non-adjacent angles that are formed when two parallel lines are intersected by a transversal. These angles are located on opposite sides of the transversal and on the inside of the parallel lines. The measure of each alternate interior angle is equal to the measure of its corresponding alternate interior angle.
Calculating Alternate Interior Angles
The measure of each alternate interior angle is equal to the measure of its corresponding alternate interior angle. When two parallel lines are intersected by a transversal, the alternate interior angles are congruent. This means that they have the same measure. To calculate the measure of an alternate interior angle, you need to know the measure of its corresponding alternate interior angle.
Example:
In the diagram below, line AB is parallel to line CD, and a transversal EF intersects both lines. What is the measure of angle 1?
Since line AB is parallel to line CD, angle 1 and angle 2 are alternate interior angles. We know that angle 2 measures 80 degrees, so angle 1 also measures 80 degrees.
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Properties of Alternate Interior Angles
Alternate interior angles have several important properties:
- Alternate interior angles are congruent.
- Alternate interior angles are located on opposite sides of the transversal.
- Alternate interior angles are located on the inside of the parallel lines.
- Alternate interior angles are supplementary to each other.
Supplementary Alternate Interior Angles
When two parallel lines are intersected by a transversal, the alternate interior angles are also supplementary. This means that the sum of the measures of two adjacent alternate interior angles is equal to 180 degrees.
Why are Alternate Interior Angles Important?
Alternate interior angles are important in geometry because they are used to prove that two lines are parallel. If two lines are intersected by a transversal and the alternate interior angles are congruent, then the lines are parallel. This is known as the Alternate Interior Angles Theorem.
People Also Ask About Define Alternate Interior Angles
What are the types of angles formed by a transversal?
When a transversal intersects two parallel lines, it creates eight different angles. The types of angles formed by a transversal include corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and vertical angles.
What is the difference between alternate interior angles and alternate exterior angles?
Alternate interior angles are located on opposite sides of the transversal and on the inside of the parallel lines. Alternate exterior angles are located on opposite sides of the transversal and on the outside of the parallel lines. These angles are congruent if and only if the lines are parallel.
What is the measure of alternate interior angles?
The measure of each alternate interior angle is equal to the measure of its corresponding alternate interior angle. When two parallel lines are intersected by a transversal, the alternate interior angles are congruent. This means that they have the same measure.