Question

ABCD is a rhombus and its diagonals intersect at O.
(i) Is ∆BOC ≅ ∆DOC? State the congruence condition used?
(ii) Also state, if ∠BCO = ∠DCO.

Answer 1

(i) Yes

\[\text{ In } ∆ BCO \text{ and } ∆ DCO: \]
\[OC = OC (\text{ common })\]
\[BC = DC (\text{ all sides of a rhombus are equal })\]
\[BO = OD (\text{ diagonals of a rhomus bisect each other })\]
\[\text{ By SSS congruence }: \]
\[ ∆ BCO \cong ∆ DCO\]
Yes
By c.p.c.t:

\[\angle BCO = \angle DCO\]