Question

Friends please answer this....

if the diagonals of a parallelogram are equal than show it is a rectangle
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Answer 1

Explanation:

WHEN THE OPPOSITE SIDES OF A PARALLELOGRAM ARE EQUAL ALONG WITH ALL ANGLES SHOULD BE CORRECTLY 90 DEGREES.

IF BOTH THE DIAGONALS ARE EQUAL AND BISECT AT 90 DEGREES MEANS , THEN WE CAN SAY THAT THE GIVE PARALLELOGRAM IS A RECTANGLE.

THANKS, THIS ANSWER MAY HELP YOU.......

Answer 2

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)