Question

If the diagonals of a parallelogram are equa, then show that it is a rectangle
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Answer 1

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

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...(2) _ Sum of consecutive interior angles on the same side of the transversal is

180

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From (1) and (2) ,

∠BAD=∠ABC=90

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∴∠A=90

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and ∠C=90

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Parallelogram ABCD is a rectangle.

solution