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Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E.
Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
congruent triangles
similar triangles
congruent rectangles
similar rectangles
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congruent triangles
Reason: In parallelogram ABCD, AB ∥ CD and AD ∥ BC, so ∠ABE = ∠CDE and ∠BAE = ∠DCE (alternate interior angles). Also AB = CD (opposite sides of a parallelogram). Thus triangles AEB and CED are congruent by ASA, which gives AE = CE and BE = DE — the diagonals bisect each other.
Reason: In parallelogram ABCD, AB ∥ CD and AD ∥ BC, so ∠ABE = ∠CDE and ∠BAE = ∠DCE (alternate interior angles). Also AB = CD (opposite sides of a parallelogram). Thus triangles AEB and CED are congruent by ASA, which gives AE = CE and BE = DE — the diagonals bisect each other.
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