Proving a Quadrilateral is a parallelogram

• Nov 28th 2008, 06:14 PM
MATHMATHmathmathMathMath
Proving a Quadrilateral is a parallelogram
If you are given that a quadrilateral has one pair of sides which are congruent and one pair of angles which are congruent, how do you prove that the quadrilateral is a parallelogram?(Thinking)
• Nov 28th 2008, 09:11 PM
Soroban
Hello, MATHMATHmathmathMathMath!

Quote:

If you are given that a quadrilateral has one pair of sides which are congruent
and one pair of angles which are congruent,
how do you prove that the quadrilateral is a parallelogram?

You can't . . . it's not true.

Code:

                  7           A o * * * * * * o B           *        30° *           *          *         *          *         *        *       *        o C       * 30° *     *  *    7   D o

We can have: . $AB = CD\,\text{ and }\,\angle B = \angle D$,

. . but $ABCD$ is not a parallelogram.