Question

Complete the proof below by matching the statement to the correct reason. *Note: There are two reasons that are the same. Use option 1 for the first time you use that reason and option 2 for the second time you use that reason. Definition of Right Angle Given (option 2 ) Definition of Complementary Angles Given (option 1) Angle Addition Postulate Substitution Property Congruent Complements Theorem

A. ˆ PQR is a right angle
B. mˆ PQR = 90°
C. mˆ PQS + mˆ SQR = ˆ PQR
D. mˆ PQS + mˆ SQR = 90°
E. ˆ PQS and ˆ SQR are complementary angles.
F. ˆ TQP and ˆ SQR are complementary angles.
G. ˆ PQS ‰… ˆ TQP

Answer 1

The proof is completed by matching each statement with its logical reasoning, from given information through the application of geometric properties such as the Definition of Complementary Angles, Angle Addition Postulate, Substitution Property, and Congruent Complements Theorem.

option b is the correct

Step-by-step explanation:

To complete the proof with the correct reasoning, we need to match each statement with the appropriate reason from the list provided. We will go through each statement step by step and identify the correct reason.

1. A. ∠ PQR is a right angle - This is a Given (option 2) fact in the proof.
2. B. m∠ PQR = 90° - This follows from the Definition of a Right Angle, which states that a right angle measures 90 degrees.
3. C. m∠ PQS + m∠ SQR = ∠ PQR - This statement is derived from the Angle Addition Postulate, which allows us to add the measures of two adjacent angles to find the measure of the larger angle.
4. D. m∠ PQS + m∠ SQR = 90° - This can be derived by the Substitution Property, where we replace m∠ PQR with 90° based on statement B.
5. E. ∠ PQS and ∠ SQR are complementary angles - This follows from the Definition of Complementary Angles (option 1), which are two angles whose measures add up to 90 degrees.
6. F. ∠ TQP and ∠ SQR are complementary angles - This could also be a result of the Definition of Complementary Angles (option 1) when used for the first time.
7. G. ∠ PQS ≠ ∠ TQP - This statement is supported by the Congruent Complements Theorem, which states that if two angles are complementary to the same angle, then they are congruent to each other.

By carefully matching each statement with the correct reason, the proof is completed accurately and thoroughly.