Question

please answer this question....

Answer 1

given : ABCD is a quadrilateral , diagonals bisect each other at right angles

to prove : ABCD  is a rhonmbus

proof : if in a quadrilateral the diagonals bisect each other it is a parallelogram

therefore ABCD is a parallelogram

now consider triangle AOD and DOC

AO = OC  (given bisector)

AO = AO  (common)

<AOD = <DOC  (given bisect at right angles)

therfore triangle AOD congruent to triangle DOC

therefore AD = DC

if in a parallelogram alternate sides are equal it is a rhombus 

THUS PROVED

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