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, \\( \angle rsu \cong \angle rqu \\). for the same reason, \\( \angle rst \cong \angle rqt \\), \\( \angle psu \cong \angle pqu \\), and \\( \angle pst \cong \angle pqt \\). each of the angle pairs are corresponding angles. therefore, corresponding angles are congruent.
parallel
perpendicular
congruent
reflected

Explanation:

Step1: Recall properties of translations

Translations are a type of transformation in geometry. One of the key properties of translations is that they preserve the orientation of a figure or a line. When a line is translated, its direction does not change.

Step2: Determine the relationship between lines \(a\) and \(b\)

Since line \(b\) is a translation of line \(a\) and translations preserve orientation, lines \(a\) and \(b\) do not intersect (because they have the same direction). In geometry, non - intersecting lines in the same plane are parallel.

Answer:

parallel