In a quadrilateral ABCD, AB is parallel to CD, and AC is a diagonal. If AB = CD, which of the following is true?
△ABC ≅ △CDA by SAS
Compare △ABC and △CDA:
(i) AB = CD — given.
(ii) ∠BAC = ∠DCA — alternate interior angles, since AB ∥ CD and AC is the transversal.
(iii) AC = CA — common side.
The matching parts are side – included angle – side, so the triangles are congruent by the SAS criterion.
(SSS would require all three sides equal — we don't know BC = DA without using the congruence we are trying to prove. ASA would require two angles, which we don't have.)
Hence, the answer is option B.
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