Properties of Parallelograms

Parallelograms have many properties. I will number them.

1. Both pairs of opposite sides are parallel.

2. Both pairs of opposite sides are equal in length.

3. Pairs of opposite angles are equal.

4. The diagonals of a parallelogram bisect each other.

5. Each diagonal of a parallelogram divides it into two congruent (equal in measure) triangles.

These should be very intuitive and easy to prove.

If you are given any of #1,2,3,4 then this is sufficient to prove the quadrilateral is a parallelogram.

For example: If we are given property 1 and we wish to prove property 3: A proof might look like this.

Property 1 implies the quadrilateral is a parallelogram, and parallelograms satisfy property 3, so property 1 implies property 3.

$[ABCD]=bh=AB * BC * \sin ABC$ where b = base, h = height.

Both expressions are easy to prove, by splitting the parallelogram into two triangles using a diagonal.