Question Regarding Geometry

Question

Quadrilateral PQRS is translated to form Quadrilateral P′Q′R′S′. Which statement must be true?

A. PQ and P′Q′ are parallel and congruent.

B. PQ and P′Q′ are parallel but not congruent.

C. PQ and P′Q′are congruent but not parallel.

D. PQ and P′Q′are neither congruent nor parallel.

Answer 1

Reading left to right PR and QS are both congruent and parallel. Every rectangle has two congruent and parallel sides.

Answer 2

Translation is a rigid transformation, so the dimensions of all sides and angles of the figure do not change after being translated. So, corresponding sides PQ and P'Q' will remain congruent. This eliminates answers B and D.

Since a translation does not change the orientation of the figure, like reflection and rotation, corresponding sides of the two quadrilaterals will be parallel on the same plane. The answer is A.