Question

quadrilateral
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then​

Answer 1

If the diagonals of a quadrilateral bisect each other at right angles , then it 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.