A quadrilateral is a parallelogram if both pairs of its opposite sides are congruent. This is because if two triangles are congruent by CPCTC (corresponding parts of congruent triangles are congruent), then their corresponding angles and sides are also congruent. To prove opposite sides of a parallelogram are congruent, show the parallelogram has two sets of congruent triangles formed by the sides.

1. Proving that a
Quadrilateral is a
Parallelogram

2. If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
CPCTC stands for "corresponding parts of congruent triangles are
congruent" and tells us if two or more triangles are congruent, then their
corresponding angles and sides are congruent as well.

3. 1. Prove that the opposite sides of a parallelogram are congruent

4. If a quadrilateral is a parallelogram, then it its opposite sides
are congruent.

6. Activity 1.