The first step is to position a parallelogram on the coordinate plane.

Label the vertices to make computations as simple as possible.

Let the vertices of the parallelogram be .

Given:                 ABCD is a parallelogram.

Prove:                 Diagonals bisect each other.

Coordinate Proof:

If the midpoint of two diagonals is same, then the diangonals bisect each other.

Find the midpoints of the diagonals and .

The midpoint formula is    .

Midpoint of    (Sunstitue )

Midpoint of                (Simplify)

Midpoint of    (Sunstitue )

Midpoint of                (Simplify)

Since the midpoint of the diagonals is same, diagonals bisect each other.

The midpoint of the diagonals is same, diagonals bisect each other.