Tests for Parallelograms

To prove a Quadrilateral is a parallelogram, you can use any one of the following tests:

1. Both pairs of opposite sides are parallel (definition).
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are congruent.
4. One pair of opposite sides is both parallel and congruent.
5. The diagonals bisect each other.

Common Mistakes

• Having only one pair of parallel sides is NOT enough (that's a trapezoid).
• Having only one pair of congruent sides is NOT enough.
• Having congruent diagonals alone does NOT prove a parallelogram (it could be an isosceles trapezoid).