1. ## 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?

2. Hello, MATHMATHmathmathMathMath!

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: .$\displaystyle AB = CD\,\text{ and }\,\angle B = \angle D$,

. . but $\displaystyle ABCD$ is not a parallelogram.