Question

ABCD is a parallelogram and it is given that diagonals AC and BD are equal then , prove that ABCD is rectangle .

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Answer 1

To Prove :-

• ABCD is a parallelogram and it is given that diagonals AC and BD are equal then , prove that ABCD is rectangle .

Proof :-

★ In ΔABD and ΔBCA

➼ AB = AB   ( Common )

➼ AD = BC ( Opposite sides of parallelogram )

➼ BD = AC ( Given )

 

  ➤ ΔADB ≌ ΔBCA by SSS criteria

⇒ ∠ DAB = ∠CBA  ( By CPCT )

→ Since , sum of adjacent angles in a parallelogram is 180° ,

  ∴ ∠DAB + ∠CBA  = 180°

→ As , ∠DAB = ∠CBA , we can write it as

 

   $\sf \therefore DAB = CBA = \dfrac{180}{2} = 90$

→ Thus , ∠A and ∠B are right angles

  ⇒ ABCD is a rectangle

    $\sf {\dag} \; Hence , Proved \; {\dag}$