Question

Show that if the diagonals of a quadrilateral bisect each other at right angles, it is a rhombus.

Answer 1

Answer:

Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O. Their corresponding parts are equal. Thus, the quadrilateral ABCD is a rhombus.

Answer 2

Step-by-step explanation:

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.