Use an indirect proof to complete the following problem.
Given: (not shown)
Prove: and cannot both be right angles.

Question

Use an indirect proof to complete the following problem.
Given:  (not shown)
Prove:  and  cannot both be right angles.

Quizplus · Accepted Answer

The Answer is Suppose that Suppose that and are both be right angles. Then and . By the Protractor Postulate, . Then . But this last statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that and cannot both be right angles.

Suppose that and are both be right angles. Then and . By the Protractor Postulate, . Then . But this last statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that and cannot both be right angles.

and

are both be right angles. Then Suppose that and are both be right angles. Then and . By the Protractor Postulate, . Then . But this last statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that and cannot both be right angles.

and

.
By the Protractor Postulate, Suppose that and are both be right angles. Then and . By the Protractor Postulate, . Then . But this last statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that and cannot both be right angles.

. Then

. But this last
statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that Suppose that and are both be right angles. Then and . By the Protractor Postulate, . Then . But this last statement contradicts the fact that the sum of teh three interior angles of a triangle is exactly 180. Thus, the supposition must be false and it follows that and cannot both be right angles.

and

cannot both be right angles.

Use an Indirect Proof to Complete the Following Problem