Thread: parallelogram

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.

This is false.

Am I right?

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.]