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In the figure, and bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

Statement    Reason

and bisect each other.    given

and     definition of bisection

m∠AEB = m∠CED    

    SAS criterion

∠ACD ≅ ∠CAB    Corresponding angles of congruent triangles are congruent.

    converse of Alternate Interior Angles Theorem

m∠BEC = m∠AED    Vertical Angles Theorem

    SAS criterion for congruence

Quadrilateral ABCD is a parallelogram.    definition of a parallelogram