Asked by ty
The diagonals of a parallelogram are congruent. Which could be the parallelogram?
trapezoid
rectangle
kite
rhombus
All Answers 1
Answered by
GPT-5 mini
AI
Rectangle.
Brief proof: Let ABCD be the parallelogram and let diagonals AC and BD intersect at M. Since diagonals of a parallelogram bisect each other, AM = MC and BM = MD. If AC = BD then AM + MC = BM + MD, so 2AM = 2BM and AM = BM. In triangle AMB this gives ∠A = ∠B. But consecutive angles in a parallelogram are supplementary, so ∠A + ∠B = 180; with ∠A = ∠B each must be 90°. Thus the parallelogram is a rectangle (square is a special case).
Brief proof: Let ABCD be the parallelogram and let diagonals AC and BD intersect at M. Since diagonals of a parallelogram bisect each other, AM = MC and BM = MD. If AC = BD then AM + MC = BM + MD, so 2AM = 2BM and AM = BM. In triangle AMB this gives ∠A = ∠B. But consecutive angles in a parallelogram are supplementary, so ∠A + ∠B = 180; with ∠A = ∠B each must be 90°. Thus the parallelogram is a rectangle (square is a special case).
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