Question

ABCD is a rhombus with centre O. Show that ∆AOB=~∆COD

Answer 1

We know that , diagonals of rhombus bisect each other.
So, OA = OC   and OB = OD    [given]
In triangle AOB and triangle COD
AO = OC                     [ GIVEN ]
∠AOB = ∠COD       [ VERTICALLY OPPOSITE ANGLES]
BO = OD                     [ GIVEN ]
So, triangle AOB is congruent to triangle COD      [ SAS ]

Answer 2

We know that , diagonals of rhombus bisect each other.

So, OA = OC   and OB = OD    (given).

In triangle AOB and triangle COD.

AO = OC   ( GIVEN ).

<AOB = <COD( VERTICALLY OPPOSITE ANGLES).

BO = OD     ( GIVEN ).

So, triangle AOB is congruent to triangle COD       (SAS Criteria ) .