# G.2.7.4 What Do We Know For Sure About Parallelograms?

- Author:
- Katie Akesson

- Topic:
- Parallelogram

The angle-side-angle theorem could be proven in a similar method to what we did for the side-angle-side theorem in the last class. Instead of spending time proving, today we are going to use the angle-side-angle theorem to prove things about parallelograms.
The angle-side-angle theorem says that two triangles are congruent when two pairs of corresponding angles and the included corresponding sides are congruent.
A parallelogram is a quadrilateral with two pairs of opposite parallel sides.

Sketch parallelogram

*ABCD*and then draw an auxiliary line to show how*ABCD*can be decomposed into 2 triangles.Prove that the 2 triangles you created are congruent, and explain why that shows one pair of opposite sides of a parallelogram must be congruent.