The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:

Question

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

According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are ________ angles, they are congruent according to the ________ Angles Theorem. Finally, angle VQT is congruent to angle WRS by the Transitive Property of Equality.

Which term accurately completes the proof?

Alternate interior
Corresponding
Same-side interior
Vertical

Answer 1

To complete the proof, the term that accurately fills the blanks in the paragraph is "Corresponding."

So the completed paragraph will read:

"Segments UV and WZ are parallel segments that intersect with line ST at points Q and R, respectively. According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Theorem. Finally, angle VQT is congruent to angle WRS by the Transitive Property of Equality."

Thus, the correct term is Corresponding.