Question

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

Answer 1

Answer:

in quadrilateral ABCD,

AC and BD are diagonals which intersect at O.

in triangle AOB and triangle AOD,

DO=OB( O is the mid point)

AO is the common side

angle AOB= angle AOD(right angle)

therefore, triangle AOB is congruence to triangle AOD

AB=AD

similarly, AB=BC=CD=AD can be proved which means

that ABCD is a rhombus.