Question

Which is NOT a way to prove a quadrilateral is a parallelogram?

a) Prove the diagonals bisect each other.
b) Prove both pairs of opposite sides are congruent.
c) Prove both pairs of opposite angles are congruent.
d) Prove one pair of opposite sides are parallel.

Answer 1

Option c) is NOT a way to prove a quadrilateral is a parallelogram because having congruent opposite angles does not guarantee that the figure is a parallelogram.

Step-by-step explanation:

In order to prove that a quadrilateral is a parallelogram, we need to satisfy all the necessary conditions. The options given are:

• a) Prove the diagonals bisect each other.
• b) Prove both pairs of opposite sides are congruent.
• c) Prove both pairs of opposite angles are congruent.
• d) Prove one pair of opposite sides are parallel.

Option c) is NOT a way to prove a quadrilateral is a parallelogram because while both pairs of opposite angles in a parallelogram are congruent, having congruent opposite angles does not guarantee that the figure is a parallelogram.