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Quadrilaterals
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13/07/2021 11:22 am
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If the diagonals of a parallelogram are equal, then show that it is a rectangle.
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13/07/2021 11:25 am
To show that, ABCD is a rectangle if the diagonals of a parallelogram are equal
Proof:
In ΔABC and ΔBAD,
AB = BA (Common)
BC = AD (Opposite sides of a parallelogram are equal)
AC = BD (Given)
Therefore, ΔABC ≅ ΔBAD [SSS congruency]
∠A = ∠B [Corresponding parts of Congruent Triangles]
∠A + ∠B = 180° (Sum of the angles on the same side of the transversal)
⇒ 2∠A = 180°
⇒ ∠A = 90° = ∠B
Therefore, ABCD is a rectangle.
Hence Proved.