Data : Diagonals of a parallelogram are equal.
To Prove : ABCD is a rectangle.
Proof: Now ABCD is a parallelogram and diagonal AC = Diagonal BD (Data)
In ∆ABC and ∆ABD,
BC = AD (Opposite sides of quadrilateral)
AC = BD (Data) AB common.
∴ ∆ABC ≅ ∆ABD (SSS postulate)
∠ABC = ∠BAD But,
∠ABC + ∠BAD = 180°
∠ABC + ∠ABC = 180°
2 ∠ABC = 180°
∴ ∠ABC = 90°
If an angle of a parallelogram is right angle, it is called rectangle.
∴ ABCD is a rectangle.