Chapter 6.3, Problem 7WE

To determine

To write: an indirect proof in paragraph form.

Explanation of Solution

Given information:

  $\Delta XYZ$ , $m\angle X=100°$

Prove:

  $\angle Y$ is not a right angle.

Calculation:

Consider the following statement:

  $\Delta XYZ$ , $m\angle X=100°$

Write an indirect proof to prove that $\angle Y$ is not a right angle.

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

Proof:

Assume temporarily that $\angle Y$ is not a right angle.

Add the two angles and get:

  $\begin{array}{c}\angle X+\angle Y=100°+90°\\ =190°\end{array}$

However, it is known that the sum of angles of a $△$ is $180°$ .

Hence, initial assumption that $\angle Y$ is a right angle is untrue.

Hence, $\angle Y$ is not a right angle.