Question

Which of the following is not a way to prove a quadrilateral is a parallelogram?

a) Show that one pair of opposite sides is both congruent and parallel.
b) Show that both pairs of opposite angles are congruent.
c) Show that both diagonals are congruent.
d) Show that consecutive angles are supplementary.

Answer 1

Option (c) showing that both diagonals are congruent, is not a valid method to prove that a quadrilateral is a parallelogram.

Step-by-step explanation:

The question asks us to identify which of the provided options is not a valid method for proving that a quadrilateral is a parallelogram. Option (c), which suggests showing that both diagonals are congruent, is not a valid method to prove that a quadrilateral is a parallelogram. Diagonals in a parallelogram are usually not congruent; instead, they bisect each other. The other options provided are valid methods for proving a quadrilateral is a parallelogram: option (a) involves showing that one pair of opposite sides is both congruent and parallel; option (b) involves showing that both pairs of opposite angles are congruent; option (d) involves showing that consecutive angles are supplementary.