Question

Figure ABCD is a parallelogram.

Parallelogram A B C D is shown. A diagonal is drawn from point A to point C.

Which sequence could be used to prove that AD = BC?

First prove TriangleABC is congruent to TriangleCDA, and then state AD and BC are corresponding sides of the triangles.
First prove TriangleABC is similar to TriangleCDA, and then state AD and BC are opposite sides of the parallelograms.
First prove ParallelogramABCD is congruent to ParallelogramCDAB, and then state AD and BC are corresponding sides of two parallelograms.
First prove ParallelogramABCD is similar to ParallelogramCDAB, and then state AD and BC are opposite sides of the parallelograms.

Answer 1

The first sequence.

Reason: AC is common. Because AB ∥ CD and BC ∥ AD, ∠ABC = ∠CDA and ∠ACB = ∠CAD. Thus ΔABC ≅ ΔCDA by ASA, and corresponding sides AD and BC are equal.