What Is a Converse in Geometry?


The converse in geometry applies to a conditional statement. In a conditional statement, the words "if" and "then" are used to show assumptions and conclusions that are to be arrived at using logical reasoning. This is often used in theorems and problems involving proofs in geometry.

If two parallel lines are intersected by a third line in two points, then the pairs of alternate interior angles are congruent. This is a conditional statement and uses the word "if" followed by the word "then" in the same sentence. When this relationship is reversed, the result is a converse statement. If a pair of alternate interior angles is congruent, then the two lines are parallel. The assumptions and the required conclusions are interchanged.