Corresponding Angles in Parallel Lines

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 a transversal, 4 pairs of corresponding angles are formed.

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.

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

Example 1

Find the value of x. The measures of the corresponding angles: 64, 7x + 1

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

So 64 = 7x + 1

Example 2

Find the value of x. Two pairs of parallel lines are the transversals to the other parallel lines. The measures of the corresponding angles: 14x - 3, 8x + 45

Two horizontal lines are parallel.
So 14x - 3 = m∠1'.

And two sloped lines are parallel.
So m∠1' = 8x + 45.

So 14x - 3 = 8x + 45.

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of the parallel lines, then the transversal is perpendicular to the other parallel line.

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.