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

Q: 2  If the diagonals of a parallelogram are equal, then show that it is a rectangle.
 

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Given: ABCD is a parallelogram with AC=BD.

To prove: ABCD is a rectangle.

Proof : In \triangleABC and \triangleBAD,   

           

                BC= AD            (Opposite sides of parallelogram)

                AC=BD              (Given )

               AB=AB               (common)

             \triangleABC \cong \triangleBAD   (By SSS)

        \angle ABC=\angle BAD             (CPCT)

and     \angle ABC+\angle BAD=180 \degree      (co - interior angles)

             2\angle BAD=180 \degree

               \angle BAD= 90 \degree

Hence, it is a rectangle.

 

 

 

 

 

 

 

 

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