Question

Prove that quadrilateral ABCD is a parallelogram. How do you know that the figure is a parallelogram? (1 point) Responses Adjacent sides of the figure are congruent. Adjacent sides of the figure are congruent. Adjacent sides of the figure are parallel. Adjacent sides of the figure are parallel. Adjacent angles of the figure are congruent. Adjacent angles of the figure are congruent. Opposite sides of the figure are congruent.

Answer 1

To prove that quadrilateral ABCD is a parallelogram, we can use one of the properties that characterize parallelograms. One of the criteria for a quadrilateral to be classified as a parallelogram is that the opposite sides are congruent.

If we show that opposite sides of quadrilateral ABCD are congruent, we can conclude that ABCD is a parallelogram.

So, the response that supports our proof is:

Opposite sides of the figure are congruent.

This means if \( AB = CD \) and \( BC = AD \), then by definition, quadrilateral ABCD is a parallelogram.