Weeks & Adkins p.214 #13

The Problem

is a quadrilateral. A straight line parallel to

meets

and

. The parallel to

through

meets

, and the parallel to

through

meets

. Prove that

is parallel to

In the diagram, drag

, or

around to change the shape of the given quadrilateral. You may also drag

along

and

, and

will move with it, according to the constructions given above.

From the setup of this diagram, we are given:

We want to prove:

How can this be proven?

For which types of can be a rhombus?

For which types of can be a rectangle?