Mathematics, 20.10.2020 20:01 kevinglvz
The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:
StepStatementsReasons
1segment UV is parallel to segment WZGiven
2Points S, Q, R, and T all lie on the same line. Given
3m∠SQT = 180°Definition of a Straight Angle
4m∠SQV + m∠VQT = m∠SQTAngle Addition Postulate
5m∠SQV + m∠VQT = 180°Substitution Property of Equality
6m∠VQT + m∠ZRS = 180°Same-Side Interior Angles Theorem
7 Substitution Property of Equality
8m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRSSubtraction Property of Equality
∠SQV ≅ ∠ZRSDefinition of Congruency
What is the missing statement for step 7?
m∠SQV + m∠VQT = 180°
m∠VQT + m∠ZRS = 180°
∠SQV + m∠VQT = m∠VQT + m∠ZRS
m∠SQV + m∠SQT = 180°
Answers: 3
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