Question

a quadrilateral ABCD has its diagonals bisecting each other at right angles show that it is a rhombus please I am in need

Answer 1

SOLUTION :

In a quadrilateral ABCD the diagonals bisect each other at 90°   (given)

To be prove :-

The quadrilateral ABCD is a rhombus

Proof :

In ΔAOD and ΔBOC

AO = OC            [given]

OD = OB            [given]

∠AOD = ∠BOC     [ (each 90° (also vertically opposite angles)]

∴ By SAS congruence condition ΔAOD ≅ ΔBOC

Hence,

by CPCT

AD = BC

∠DAO = ∠OCB

∠ADO = ∠OBC

SO,

∴ AD║BC

similarly in other two triangle also

So,

We get

AD║BC and AB║DC

So,

The sides of the quadrilateral is parallel to each side

And the diagonals bisect each other a 90°

So,

It is the property of rhombus

Hence,

The quadrilateral is a rhombus.

Answer 2

Step-by-step explanation:

thanks for free points ok

thanks for free points ok

thanks for free points ok