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Based on the diagram above, the following relation holds true.
If ∠A≅∠B or ∠C≅∠D, then the trapezoid ABCD is isosceles.
Consider an auxiliary line that passes through C and is parallel to AD. Let E be the intersection point of this line and AB.
By the Converse Isosceles Triangle Theorem, △BEC is isosceles. Therefore, EC and BC are congruent. Lastly, using the Transitive Property of Congruence once again, it is obtained that AD≅BC. Consequently, ABCD is an isosceles trapezoid.