Question

show that if the diagonals of a quadrilateral bisects each other at right angles, then it is a rhombus.​

Answer 1

Answer:

Take quadrilateral ABCD, AC and  BD are diagonals which intersect at O.

In ΔAOB and ΔAOD

DO = OB   (∵ O is the midpoint)

AO = AO    (∵ common side)

∠AOB = ∠AOD  (∵Right angle)

So, Δ AOB ≅ ΔAOD

So, AB = AD

Similarly, AB = BC = CD = AD can be proved which means that ABCD  is a rhombus.

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