# Alternate Interior Angles in Parallel Lines

How to solve alternate interior angles in parallel lines problems: definition, theorem, examples, and their solutions.

## Definition

By two lines and a transversal,

2 pairs of alternate interior angles are formed.

(same colored angles)

## Theorem

If a transversal passes through parallel lines,

then a pair of alternate interior angles is congruent.

(= Same colored angles are congruent.)

## Example 1

These two horizontal lines are parallel.

So the given alternate interior angles are congruent.

So 6*x* - 7 = 59.

## Example 2

Draw an auxiliary line (dashed line)

that is parallel to the horizontal lines.

Then the blue angles are congruent.

And the purple angles are also congruent.

So *x* = 53 + 34.