Isosceles Trapezoid Diagonals

Use coordinate geometry to prove that both diagonals of an isosceles trapezoid are congruent. That is, write a coordinate geometry proof that formally proves what this applet informally illustrates. Be sure to assign appropriate variable coordinates to your isosceles trapezoid's vertices! (The maximum number of variable coordinates your coordinate setup should have is 3.)
Now prove this same theorem true using the format of a 2-column proof or a paragraph proof. Hint: This proof will contain at least one pair of congruent triangles.