Definition

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e., the transversal).

For example, in the figure below, angle p and angle w are corresponding angles.

Corresponding Angles Examples and Types

Examples of corresponding angles are any angles formed on the opposite side of the transversal. These can be of two types:

• Corresponding angles formed by parallel lines and transversals
• Corresponding angles formed by non-parallel lines and transversals

Corresponding Angles Formed by Parallel Lines and Transversals

If a transversal crosses two parallel lines, then the corresponding angles formed have equal measures.

Corresponding Angles Theorem

The corresponding angles theorem states: "If a line intersects two parallel lines, then the corresponding angles are congruent (equal)."

The Converse of the Corresponding Angles Theorem

The converse states: "If the corresponding angles are congruent, then the two lines are parallel."

Important Notes on Corresponding Angles

• When two parallel lines are intersected by a third one, the angles that occupy the same relative position at different intersections are called corresponding angles.
• Corresponding angles are congruent with each other.
• If the corresponding angles in the two intersection regions are congruent, then the two lines are parallel.