Determine the missing information in the paragraph proof.

Question

Given: Lines a and c intersect at point S, creating 4 angles.
Prove: Corresponding angles are congruent.

Lines a and c intersect at point S. Line c is diagonal and also contains points R, Q, P. Line a is horizontal and also contains points U, T.

We are given that lines a and c intersect at point S. Translate line a down line c until point S reaches point Q. Call the new line through Q line b. Because translations preserve orientation, lines a and b are ________. Because translations preserve angle measure, ∠RSU ≅ ∠RQU'. For the same reason, ∠RST ≅ ∠RQT', ∠PSU ≅ ∠PQU', and ∠PST ≅ ∠PQT'. Each of the angle pairs are corresponding angles. Therefore, corresponding angles are congruent.

parallel
perpendicular
congruent
reflected

Answer 1

In the paragraph proof you provided, the missing information should be "parallel." Here is the completed section:

"Because translations preserve orientation, lines a and b are parallel."

This is because if a line is translated along another line while maintaining the orientation, the two lines will remain parallel to each other.