If the diagnnals of a parallelogram are equal, then show that it's a rectangle
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Step-by-step explanation:
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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
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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.
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