Consider a pair of lines cut by a transversal. The pairs of angles with different vertices that lie on the same position relative to the vertex are called corresponding angles. In the diagram, $\angle 1$ and $\angle 5$ are corresponding angles because they are both northeast of their vertices. Alternatively, two angles are corresponding angles if they meet the following conditions.

• One angle is exterior and the other is interior.
• The angles have different vertices.
• The angles lie on the same side of the transversal.

In the diagram, four pairs of angles can be identified as corresponding angles.

Pair	Position Relative to the Vertex	Position Relative to the Transversal
$\angle 1$ and $\angle 5$	Northeast	Right
$\angle 2$ and $\angle 6$	Northwest	Left
$\angle 3$ and $\angle 7$	Southwest	Left
$\angle 4$ and $\angle 8$	Southeast	Right

If two parallel lines are cut by a transversal, then the corresponding angles are congruent. The same logic in reverse can be applied. If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

If	Then
${\ell }_1\parallel {\ell }_2$	$\angle 1\cong \angle 5,$ $\angle 2\cong \angle 6,$ $\angle 3\cong \angle 7,$ and $\angle 4\cong \angle 8$
$\angle 1\cong \angle 5,$ $\angle 2\cong \angle 6,$ $\angle 3\cong \angle 7,$ or $\angle 4\cong \angle 8$	${\ell }_1\parallel {\ell }_2$

These statements are supported by the Corresponding Angles Theorem and its converse.