Question

if two opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
a. true
b. false

Explanation:

The definition of a parallelogram includes that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then it is a parallelogram. Here, the statement says "if two opposite sides of a quadrilateral are parallel and congruent" – wait, actually, the standard theorem is about both pairs, but if one pair of opposite sides is parallel and congruent, we can prove the quadrilateral is a parallelogram (by using triangle congruence and alternate interior angles to show the other pair is also parallel). Wait, the original statement: "If two opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram" – actually, the correct theorem is that if one pair of opposite sides is both parallel and congruent, then the quadrilateral is a parallelogram. So the statement here (assuming it's "two" as in one pair? Wait, maybe a typo, but the key is that the theorem states that if a quadrilateral has one pair of opposite sides parallel and congruent, it's a parallelogram. So the statement is True.

Answer:

A. True