Question

show that if the diagonal of a quadrilateral are equal and bisect each other at right angle , then it is a rhombu​

Answer 1

Take quadrilateral ABCD

> AC and BD are diagonals which intersect at O.

In △AOB and △AOD

DO=OB ∣ O is the midpoint

AO=AO ∣ Common side

∠AOB=∠AOD ∣ Right angle

So, △AOB≅△AOD

So, AB=AD

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

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