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
Angle Addition Postulate
Definition of Angle Bisector

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Gia Bảo 5 months 2021-09-02T21:27:59+00:00 1 Answers 13 views 0

Answers ( )

  1. Latifah
    0
    2021-09-02T21:29:00+00:00
    Reply

    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°.

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