# What is the reason for step 3 in the two column proof below 1. ZPQR is a right angle 1. Given 2. MZPQR = 90° 2. Defi

Question

What is the reason for step 3 in the two column proof below
1. ZPQR is a right angle
1. Given
2. MZPQR = 90°
2. Definition of Right Angle
3. m_PQS + MZSQR = m_PQR
3. ?
4. MZPQS + m_SQR = 90°
4. Substitution Property of Equality
5. ZPQS and 2SQR are complementary 5. Definition of Complementary Angles
Definition of Congruent Angles
Vertical Angles Congruence Theorem
Definition of Angle Bisector

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1 year 2021-09-02T21:27:59+00:00 1 Answers 20 views 0

The correct option is;

Step-by-step explanation:

The given two column proof can be presented as follows;

Statement                      [tex]{}[/tex]                          Reason

1. ∠PQR is a right angle      [tex]{}[/tex]                     Given

2. m∠PQR = 90°       [tex]{}[/tex]                                Definition of Right Angle

3. m∠PQS + m∠SQR = m∠PQR      [tex]{}[/tex]         Angle Addition Postulate

4. m∠PQS + m∠SQR = 90°      [tex]{}[/tex]                 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°.