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.
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.
options: parallel, perpendicular, congruent, reflected

Explanation:

A translation is a rigid transformation that preserves the direction (orientation) of a line. When line \( a \) is translated to form line \( b \), since translations preserve orientation, the lines \( a \) and \( b \) will have the same slope (or direction) and thus be parallel. Perpendicular lines have slopes that are negative reciprocals, congruent refers to angle or segment measures, and reflected implies a different transformation (reflection) which changes orientation. So the correct term is parallel.

Answer:

A. parallel