Proving a Trapezoid

Given that ABCD is a quadrilateral and that W two-thirds of the way from B to A, X is two-thirds of the way from B to C, Y is one-third of the way from D to C and Z is one-third of the way from D to A. We want to prove that WXYZ is a trapezoid.
1. Given slider a, what is the equation we will need to use to show/prove WXYZ is a trapezoid? (Think of the properties/definition of a trapezoid. When are two vectors parallel?)
2. Is there an a value for slider a that makes your equation true? What does this mean?

Catherine O'Neill, Created with GeoGebra