Question

If the diagonals of a quadrilateral bisect each at right angle, then it is a rhombus (PROVE please) ?

Answer 1

heya..

here is your answer...

let us take a quadrilateral ABCD diagonals AC and BD bisect each other at right angle. We have to prove that  

A B = B C = C D = A D

AB=BC=CD=AD

In ΔAOB and ΔAOD

D O = O B

DO=OB (O is the midpoint)

A O = A O

AO=AO (common side)

∠ A O B = ∠ A O D

∠AOB=∠AOD (right angle)

So,  

Δ A O B ≅ Δ A O D

ΔAOB≅ΔAOD

So,  

A B = A D

AB=AD

Similarly  

A B = B C = C D = A D

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

it may help you..

Answer 2

Hey mate

here's the answer...

Hope it helps ⭐