Consecutive Interior Angles Converse Theorem

This page explains the 'Consecutive Interior Angles Converse Theorem'. Use this section to learn this theorem in a simple way. This theorem states that if two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are said to be parallel. This can be proved by showing that the angles inside the two lines and on the Same side of the transversal are supplementary (add to 180 degrees) than you can conclude the lines are parallel.

If a transversal intersects two lines in such a way that a pair of consecutive interior angle are supplementary, then the two lines are parallel.

Consecutive Interior Angles Converse Theorem
Given:

A transversal intersects two lines AB and CD at F and G respectively, such that ∠(c) and ∠(f) is a pair of consecutive interior angle and ∠(c) + ∠(f) = 180°

To Prove: AB is parallel to CD

Consider the line AB
∠(c) + ∠(d) = 180°
∠(c) + ∠(d) = ∠(c) + ∠(f)
∠(d) = ∠(f)
Since, ∠(d) and ∠(f) are alternate angle and are equal.
Therefore, AB is parallel to CD.

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In simple words it is a theorem used to prove that two lines crossed by a transversal are parallel. We say this is a converse theorem, because it is similar to an inverse function. Usually you are given two parallel lines; but here you are given with two lines and have to prove that they are parallel. Hence it is called as converse.

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