# Corresponding Angles in Parallel Lines

How to solve corresponding angles in parallel lines problems: definition, theorem, examples and their solutions, and perpendicular transversal theorem.

## Definition

A transversal is a line that passes through two lines.

By two lines and a transversal,

4 pairs of corresponding angles are formed.

(same colored angles)

## Theorem

If a transversal passes through parallel lines,

then a pair of corresponding angles is congruent.

(= Same colored angles are congruent.)

## Example 1

These two horizontal lines are parallel.

So the given corresponding angles are congruent.

So 64 = 7*x* + 1

## Example 2

Two horizontal lines are parallel.

So 14*x* - 3 = m∠1'.

And two sloped lines are parallel.

So m∠1' = 8*x* + 45.

So 14*x* - 3 = 8*x* + 45.

## Perpendicular Transversal Theorem

If a transversal is perpendicular to

one of the parallel lines (top line),

then the transversal is perpendicular to

the other parallel line (bottem line).

It is the right angle version

of the corresponding angles in parallel lines.