Alternate Interior Angles in Parallel Lines

Alternate Interior Angles in Parallel Lines

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

Definition

Alternate Interior Angles: 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.

If a transversal passes through parallel lines,
then a pair of alternate interior angles is congruent.
(= Same colored angles are congruent.)

Example 1

Find the value of x. The measures of the alternate interior angles in parallel lines: 6x - 7, 59

These two horizontal lines are parallel.
So the given alternate interior angles are congruent.

So 6x - 7 = 59.

Example 2

Find the value of x. The measures of the given angles in parallel lines: 53, 34

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.