If the diagonals of a parallelogram are equal than show it is a rectangle
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PLSS MRK BRAINLIEST
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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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