Question

Show that it the diagonals af a quadrilateral bisect each other at right angles, then it is a rhombus .
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Answer 1

Answer:

Take quadilateral ABCD , AC and BD are diagnoals which intersect at O .

in triangle AOB and triangle AOD

DO = OB | O is midpoint

AO = AO | Common side

<AOB = <AOD | Right angle

so, triangle AB = AD

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

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