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.
reflected
congruent
perpendicular
parallel

Explanation:

Translation is a type of transformation that slides a figure without rotating or resizing it. One of the key properties of translation is that it preserves the orientation of the figure. When two lines have the same orientation (after a translation), they are parallel. Since line \(a\) is translated to get line \(b\) and translations preserve orientation, by the definition of parallel lines (lines that never intersect and have the same slope/orientation in a plane - in the context of transformations, same orientation from translation implies parallel), lines \(a\) and \(b\) must be parallel.

Answer:

parallel