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If the diagonals of a parallelogram are equal in length,show that the parallelogram is a rectangle |
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Answer» Given: ABCD is a parallelogram and AC = BD To prove: ABCD is a rectangle Proof: In Δ ACB and ΔDCB AB = DC _____ Opposite sides of parallelogram are equal BC = BC _____ Common side AC = DB _____ Given Therefore, Δ ACB ≅ ΔDCB by S.S.S TEST ANGLE ABC = Angle DCB ______ C.A.C.T Now, AB ║ DC _______ Opposite sides of parallelogram are parallel Therefore, Angle B + Angle C = 180 degree (Interior angles are supplementary) Angle B + Angle B = 180 2 Angle B = 180 degree Angle B = 90 degree Similarly, we can prove that, Angle A = 90 degree, Angle C = 90 degree and Angle D = 90 degree. Therefore, ABCD is a rectangle. (Refer to the attachment for the figure) |
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