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Alternate Interior Angles

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Alternate Interior Angles

Study Guide

Key Definition

The term $\text{Alternate Interior Angles}$ is often used when two lines are cut by a third line, a transversal. The pairs of alternate interior angles are congruent if the two lines are parallel.

Important Notes

Two lines are parallel if they never intersect.
A transversal is a line that intersects two or more lines at distinct points.
$\angle 2 \cong \angle 8$ and $\angle 3 \cong \angle 5$ if lines are parallel.
Alternate interior angles are congruent.

Mathematical Notation

$\angle$ represents an angle.

$\cong$ means congruent or equal in measure.

Remember to use proper notation when solving problems.

Why It Works

The property of alternate interior angles being congruent works because of the way lines and transversals intersect in Euclidean geometry. When two parallel lines are intersected by a transversal, corresponding angles are equal. Since alternate interior angles lie on opposite sides of the transversal within the parallel lines, they are non-adjacent corresponding angles and therefore equal.

Remember

The pairs of alternate interior angles are congruent if the two lines are parallel. That is, $\angle 2 \cong \angle 8$ and $\angle 3 \cong \angle 5$.

Quick Reference

Alternate Interior Angles:$\angle 2 \cong \angle 8, \angle 3 \cong \angle 5$

Understanding Alternate Interior Angles

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Video explanation of this concept

Beginner

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Beginner Explanation

Alternate Interior Angles are the angles that are formed on the inside of two parallel lines and on opposite sides of the transversal.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

In the standard diagram of two parallel lines cut by a transversal (angles 1–8 numbered accordingly), which of the following angles are alternate interior angles?

Real-World Problem

Question Exercise

Intermediate

Parking Lot Lines

In a parking lot, two rows of cars are parked parallel to each other. A car parked diagonally forms a transversal. If one of the alternate interior angles formed is 75 degrees, what is the measure of the other angle?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Are alternate interior angles always equal? Explain your answer.

Challenge Quiz

Single Choice Quiz

Advanced

In the standard diagram of two parallel lines cut by a transversal (angles 1–8 numbered accordingly), if $\angle 3$ is $45^\circ$, what is $\angle 5$?

Recap

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