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.
parallel
perpendicular
congruent
reflected

Explanation:

Translation is a type of transformation that slides a figure without rotating or resizing it. When a line is translated, the direction of the line (its orientation) remains the same. In geometry, two lines with the same orientation are parallel. Since line \(b\) is a translation of line \(a\), and translations preserve orientation, lines \(a\) and \(b\) must be parallel.

Answer:

parallel