91Ó°ÊÓ

An indirect proof is a proof wherein you begin by assuming temporarily that the desired conclusion is not true which then by reasoning logically reaches to a certain contradiction or some other known fact.

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction.

3. Point out that the assumption was wrong and the conclusion must then be true.

Consider the following: Transversal t cuts lines a and b; $m∠1≠m<2$.

In order to write an indirect proof to prove that $a\cancel{\left|\right|}b$assume temporarily that the conclusion above is untrue.

Proof: Assume temporarily that $a$is parallel to $b$, that is., $a\left|\right|b$.

If the two lines are parallel, then $m∠1$should be equal to $m∠2$as alternate exterior angles are equal, however, it is given that $m∠1≠m∠2$. Therefore, the assumption $a$is parallel to $b$, that is., $a\left|\right|b$is wrong and therefore, $a\cancel{\left|\right|}b$,

Hence, $a$ is not parallel to $b$.