# If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Let ABCD be a parallelogram. To show that ABCD is a rectangle,

We have to prove that: One of its interior angles is 900 In ΔABC and ΔDCB,

AB = DC (Opposite sides of a parallelogram are equal)

BC = BC (Common)

AC = DB (Given that the diagonals are equal)

ΔABC ΔDCB (By SSS Congruence rule)

ABC = DCB

It is known that the sum of the measures of angles on the same side of transversal is 1800

ABC + DCB = 1800 (AB || CD)

ABC + ABC = 1800

ABC = 900

Since ABCD is a parallelogram and one of its interior angles is 900, ABCD is a rectangle.

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