Cassius knows that AE¯¯¯¯¯¯¯¯≅CE¯¯¯¯¯¯¯¯ and BE¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯. How can Cassius prove that quadrilateral ABCD is a parallelogram?

A. Since AE¯¯¯¯¯¯¯¯≅CE¯¯¯¯¯¯¯¯ and BE¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯, then E is the midpoint of AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. Cassius can use that to show that AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are parallel, and thus quadrilateral ABCD is a parallelogram.

B. Since AE¯¯¯¯¯¯¯¯≅CE¯¯¯¯¯¯¯¯ and BE¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯, then E is the midpoint of AC¯¯¯¯¯¯¯¯ and BD¯¯¯¯¯¯¯¯. Cassius can use that to show that AC¯¯¯¯¯¯¯¯ and BD¯¯¯¯¯¯¯¯ bisect each other, and thus quadrilateral ABCD is a parallelogram.

C. Since AE¯¯¯¯¯¯¯¯≅CE¯¯¯¯¯¯¯¯ and BE¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯, then Cassius can use the Vertical Angles Theorem to show ∠AEB≅∠CED, and thus quadrilateral ABCD is a parallelogram.

D. Since AE¯¯¯¯¯¯¯¯≅CE¯¯¯¯¯¯¯¯ and BE¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯, then E is the midpoint of AC¯¯¯¯¯¯¯¯ and BD¯¯¯¯¯¯¯¯. Cassius can use that to show that AC¯¯¯¯¯¯¯¯ and BD¯¯¯¯¯¯¯¯ are congruent, and thus quadrilateral ABCD is a parallelogram.