Question

Use the figure and flowchart proof to answer the question:

Segments UV and WZ are parallel segments that intersect line ST at points Q and R, respectively


Which property of equality accurately completes Reason C?
(Also where the fudge is reason C?)

Addition Property of Equality

Division Property of Equality

Substitution Property of Equality

Subtraction Property of Equality

Answer 1

Answer: Subtraction Property of Equality

Explanation:

Statement corresponds to Reason C : ∠SQV+∠VQT-∠VQT=∠VQT+∠ZRS-∠VQT.

Statement jut above this statement: ∠SQV+∠VQT=∠VQT+∠ZRS.

Here, Subtraction Property of Equality is used to subtract ∠VQT from both sides to get statement corresponds to Reason C.

∴ Property of equality accurately completes Reason C =Subtraction Property of Equality

• Subtraction Property of Equality says that whenever we subtract same number of expression from both sides of the equation, the equality remains the same.

Answer 2

Subtraction Property of Equality

Explanation:

1.
`\overline{UV} \parallel \overline{WZ}` - Given

2.
`m\angle VQT+m\angle ZRS=180^(\circ)` - Consecutive Interior Angles (Reason A)

3.
`m\angle SQV+m\angle VQT=m\angle VQT+m\angle ZRS` - Substitution Property of Equality (Reason B)

4.
`m\angle SQV+m\angle VQT-m\angle VQT=m\angle VQT+m\angle ZRS-m\angle VQT` - Subtraction Property of Equality (Reason C)

5.
`m\angle SQV=m\angle ZRS\Rightarrow \angle SQV\cong \angle ZRS`