Chapter 6.3, Problem 9WE

To determine

To write: an indirect proof in paragraph form.

Answer to Problem 9WE

  $a$ is not parallel to $b$ .

Explanation of Solution

Given information:

Transversal $t$ cuts lines $a$ and $b$ ;

  $m\angle 1\ne m\sum 2$

Prove:

  $a\parallel b$

Given figure,

  

Calculation:

Consider the following statement:

Transversal $t$ cuts lines $a$ and $b$ .

Write an indirect proof to prove that $a$ is not parallel to $b$ .

An indirect proof is initiated by assuming temporarily that need to prove is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that $a$ is parallel to $b$ .

However, it is given that $m\angle 1\ne m\sum 2$

If the two lines are parallel,

Then $m\angle 1$ should be equal to $m\angle 2$ as alternate exterior angles are equal

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