Question

which statement proves that a quadrilateral is a parallelogram?
a) both pairs of opposite angles are congruent.
b) one pair of opposite sides is congruent.
c) the diagonals are congruent.
d) the diagonals are perpendicular.

Explanation:

• Option B: A single congruent pair of opposite sides is not sufficient to prove a quadrilateral is a parallelogram (it could be a trapezoid).
• Option C: Congruent diagonals are a property of rectangles (a type of parallelogram) but also of isosceles trapezoids, so this does not exclusively prove a parallelogram.
• Option D: Perpendicular diagonals are a property of rhombuses/kites, not all parallelograms.
• Option A: A quadrilateral with both pairs of opposite angles congruent must be a parallelogram, as this satisfies a standard parallelogram theorem.

Answer:

A) Both pairs of opposite angles are congruent.