Question

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

Answer 1

Answer:

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Step-by-step explanation:

ANSWER IS IN THE PIC

Answer 2

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Given :

In parallelogram ABCD, AC = BD

To prove :

Parallelogram ABCD is rectangle.

Proof :

In △ACB and △BDA,

AC = BD [ Given ]

AB = BA [Common]

BC = AD [ Opposite sides of the parallelogram ABCD]

△ACB ≅△BDA∣SSS Rule

∴ ∠ABC=∠BAD...(1) CPCT

Again AD ∥ ∣ Opposite sides of parallelogram ABCD

AD ∥BC and the traversal AB intersects them.

∴ ∠BAD+∠ABC=180∘ ...(2)

Sum of consecutive interior angles on the same side of the transversal is 180∘.

From (1) and (2) ,

∠BAD=∠ABC=90∘

∴ ∠A=90∘ and ∠C=90°

Parallelogram ABCD is a rectangle.