Question

What is the reason for step 3 in the two column proof below

Answer 1

Answer:

The correct option is;

Angle Addition Postulate;

Step-by-step explanation:

The given two column proof can be presented as follows;

Statement                      ${}$                          Reason

1. ∠PQR is a right angle      ${}$                     Given

2. m∠PQR = 90°       ${}$                                Definition of Right Angle

3. m∠PQS + m∠SQR = m∠PQR      ${}$         Angle Addition Postulate

4. m∠PQS + m∠SQR = 90°      ${}$                 Substitution property of equality

5. ∠PQS and ∠SQR are complementary Definition of complementary angles

Given that the angle m∠PQR has angles m∠PQS and m∠SQR arranged adjacent to each other while sharing the same boundary segment, QS we have by the angle addition postulate;

m∠PQR is the sum of the angles m∠PQS and m∠SQR, therefore;

m∠PQR = m∠PQS + m∠SQR = 90°.