Question

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

Answer 1

The missing statement for step 5 is

B. m∠SQV + m∠VQT = 180°

What is substitution property of equality?

The substitution property of equality states that if a = b, then b can be substituted for a and vice versa in any expresion without changing the truth of the equation.

If two values are equal, you can replace one with the other in any mathematical statement.

Using the figure we an see that m∠SQV + m∠VQT = m∠SQT and it has earlier been shown that m∠SQT = 180. Then by substitution we have that

B. m∠SQV + m∠VQT = m∠SQT

Answer 2

Substitution property of Equality:

`\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}`