Question

Determine the missing information in the paragraph proof.

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

parallel

A translation is a rigid motion that preserves direction/slope, so the image of line a under the translation is a line b parallel to a.