We are given that lines A and c intersect at point cap s Translate line A down line c until point cap s reaches point cap q Call the new line through cap q line b Because translations preserve orientation, lines A and b are ________. Because translations preserve angle measure, angle RSU is congruent to angle RQU prime For the same reason, angle RST is congruent to angle RQT prime , angle PSU is congruent to angle PQU prime , and angle PST is congruent to angle PQT prime Each of the angle pairs are corresponding angles. Therefore, corresponding angles are congruent.
A translation moves every point the same distance in the same direction, so it preserves a line’s orientation. The translated image of line A, called line b, therefore has the same direction as line A, making the lines parallel. This matches choice B, “parallel.” The angle statements also follow because translations preserve angle measure.
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