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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.
 

Answers (1)

best_answer

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.

 

 

 

 

 

 

 

 

Posted by

seema garhwal

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