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Expert-verified Found in: Page 216 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Write an indirect proof in paragraph form.Given: Transversal t cuts lines a and b; $m\angle 1\ne m<2$Prove: $a\overline{)||}b$ An indirect proof in paragraph form is-

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

If the two lines are parallel, then $m\angle 1$ should be equal to $m\angle 2$ as alternate exterior angles are equal, however, it is given that role="math" localid="1638446966534" $m\angle 1\ne m\angle 2$. Therefore, the assumption a is parallel to b, that is., $a\parallel b$ is wrong and therefore, $a\overline{)||}b$.

Hence, a is not parallel to b.

See the step by step solution

## Step 1. Define concept of indirect proof of the statement

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.

## Step 2. Steps of writing an indirect proof

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.

## Step 3. State the indirect proof

Consider the following: Transversal t cuts lines a and b; $m\angle 1\ne m<2$.

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

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

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

Hence, a is not parallel to b. ### Want to see more solutions like these? 