Question

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

Answer 1

In the given quadrilateral ABCD diagonals AC and BD bisect each other at right angle. We have to prove that AB=BC=CD=AD

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

Answer 2

Show the opposite triangles formed by the diagonals of the quadrilateral congruent and all the sides will be equal according to cpct.