Question

ABCD is a rhombus whose diagonals intersect at O show that angle AOB equal to angle C O D

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

Hi dear here is your solution

We known that, diagonals of rhombus bisect each other.
so, OA=OC and OB=[Given]
In triangle AOB and triangle COD
AO=OC[Given]
<AOB=<COD [ VERTICALLY
OPPOSITE ANGELES]
BO=OD [Given]


So, triangle AOB is congruent to triangle COD[SAS]

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