Hello, Veronica1999!

If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent.

What is the converse of this statement? .Is it true?

If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.

Yes, this is the converse.

This is false. . No, it is true.

We have quadrilateral with

Draw diagonal

Let

Code:

D * - - - - - * C
/ 2 * /
/ * /
/ * /
/ * /
/ * 1 /
A * - - - - - * B

In triangles and

Hence: .

Therefore: .

Since and is a parallelogram.

[Theorem: if two sides of a quadrilateral are equal and parallel,

. . . . . . . . the quadrilateral is a parallelogram.]