1.

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

Answer»

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.


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