Question

The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:


Step Statements Reasons
1 segment UV is parallel to segment WZ Given
2 Points S, Q, R, and T all lie on the same line. Given
3 m∠SQT = 180° Definition of a Straight Angle
4 m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
5 Substitution Property of Equality
6 m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
7 m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
8 m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency


What is the missing statement for step 5?
m∠SQV = m∠SQT
m∠SQV + m∠VQT = 180°
m∠SQV + m∠SQT = m∠VQT
m∠SQV + m∠SQT = 180°

Answer 1

The missing statement for step 5 in the proof is:

**m∠SQV + m∠VQT = m∠SQT**.

This statement follows from step 4, where we applied the Angle Addition Postulate to conclude that the sum of angles \(\angle SQV\) and \(\angle VQT\) equals the straight angle \(\angle SQT\). Thus, step 5 should state that \(m\angle SQV + m\angle VQT = m\angle SQT\).