Question

Write a paragraph proof to prove the

statement.
Given: mZQRS = 90°
Given: ZRTS = ZQRT
Prove: ZRTS and ZTRS are complementary."

Answer 1

Angles ZRTS and ZTRS are complementary because they sum to 90°, filling the gap in the right angle formed with angle ZQRT, which is congruent to ZRTS.

Step-by-step explanation:

To prove that angles ZRTS and ZTRS are complementary, we start with the given information: mZQRS = 90° and ZRTS = ZQRT. Given that ZQRT and ZQRS form a right angle, and ZRTS is congruent to ZQRT, it follows that ZRTS plus ZTRS must sum to 90° to fill the gap left by ZRTS in the right angle.

By definition, two angles are complementary if the sum of their measures is 90°. As we have established that the angle ZQRT (which is equal to ZRTS) and ZTRS combine to complete the right angle formed by ZQRT and ZQRS, we can conclude that ZRTS and ZTRS are indeed complementary. This proof relies on congruent angles and the definition of complementary angles, hence completing the paragraph proof.