Question

ABCD is a rhombus and its diagonals intersect at O.

(i) Is $\Delta BOC\cong \Delta DOC$? State the congruence condition used?
(ii) Also state, if $\angle BCO=\angle DCO$.

Answer 1

In rhombus ABCD, diagonals AC and BD bisect each other at O.

(i) Now in $\Delta BOC$ and $\Delta DOC$
OC = OC (Common)
BC = CD (Sides of rhombus)
OB = OC
($\because$ Diagonals bisect each other at O)
$\therefore \Delta BOC\cong \Delta DOC$ (SSS. condition)
(ii) $\angle BCO=\angle DCO$ (c.p.c.t)