Corresponding angles are congruent to each other.When two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are called corresponding angles to each other.This is the converse of the corresponding angle theorem. What if a transversal intersects two parallel lines and the pair of corresponding angles are also equal? Then, the two lines intersected by the transversal are said to be parallel. The corresponding angles converse theorem would be, “If the corresponding angles in the two intersection regions are congruent, then the two lines are said to be parallel. The Converse of Corresponding Angles Theorem When the transversal intersects two non-parallel lines, the corresponding angles are not congruent.Īccording to the corresponding angles theorem, the statement “ If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent” is true either way.

Surprisingly, corresponding angles formed by the transversal that intersects two parallel lines are angles that are congruent. The word “corresponding” itself suggests that the angles can be either inequivalent or equivalent (congruent). Now that we have understood the definition of corresponding angles, we can figure out whether any two given angles are corresponding or not in any given diagram. Therefore, we can say that angles 1 and 2 are corresponding angles. Hence, our corresponding angles definition seems to be justified. From the diagram, we can see that angles 1 and 2 are occupying the same relative position - the upper right side angles in the intersection region.The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.Īccording to geometry, and the definition of the corresponding angles, we can say that:

Supplementary angle theorem