The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent: Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD.

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct a diagonal from A to C with a straightedge. . Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the Alternate Interior Angles Theorem. Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.