Question

ABCD is a Rhombus whose diagonals intersect at o.show that triangle AOB=triangle COD.

Answer 1

angle AOB=angle COD as they are vertically opposite angles.
and also,
OB=OB
AB=CD
OA=OC
hence, also can be proved by congruency

Answer 2

given-ABCD is a rhombus
AB=CD
AC=BD
TO PROVE-TRIANGLE AOB =TRIANGLE COD
PROOF- IN TRIANGLE AOB AND TRIANGLE COD
AB=CD{SIDES OF RHOMBUS}
ANGLE AOB =ANGLE COD{VERTIVCALLY OPPOSITE ANGLES}
OA =OD{AD AND BC ARE BISECTORS AND BISECT AT O }
THEREFORE TRIANGLE AOB=TRIANGLE COD
HENCE PROVED