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Use the figure to answer the question that follows:

Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively

When written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:


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

Use the figure to answer the question that follows: Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively When written i class=
Use the figure to answer the question that follows: Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively When written i class=
Use the figure to answer the question that follows: Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively When written i class=

Answer :

Substitution property of Equality:

[tex]\begin{gathered} a=b \\ \\ c+d=a \\ \\ \text{Then:} \\ c+d=b \\ \\ \\ \\ m\angle\text{SQT}=180 \\ m\angle\text{SQV}+m\angle\text{VQT}=m\angle SQT \\ \\ Substitution\text{ property of equality:} \\ m\angle\text{SQV}+m\angle\text{VQT}=180 \end{gathered}[/tex]

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