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The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:StepStatementsReasons1segment UV is parallel to segment WZGiven2Points S, Q, R, and T all lie on the same line.Given3m∠SQT = 180°Definition of a Straight Angle4m∠SQV + m∠VQT = m∠SQTAngle Addition Postulate5m∠SQV + m∠VQT = 180°Substitution Property of Equality6m∠VQT + m∠ZRS = 180°Same-Side Interior Angles Theorem7Substitution Property of Equality8m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQTm∠SQV = m∠ZRSSubtraction Property of Equality∠SQV ≅ ∠ZRSDefinition of CongruencyWhat 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°

Answer :

Given:

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

To find:

The missing statement is in step 7.

Explanation:

From the step 5,

[tex]m∠SQV+m∠VQT=180°[/tex]

From the step 6,

[tex]m∠VQT+m∠ZRS=180°[/tex]

Using the substitution property of equality,

We can write it as in step 7,

[tex]∠SQV+m∠VQT=m∠VQT+m∠ZRS[/tex]

Final answer:

The missing statement in step 7 is,

[tex]∠SQV+m∠VQT=m∠VQT+m∠ZRS[/tex]

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