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Understanding Shapes – II (Special Types of Quadrilaterals) — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Shapes – II (Special Types of Quadrilaterals)5 Marks
Question
$\text{ABCD}$ is a rhombus and its diagonals intersect at $O$.
$i.$ Is $\triangle\text{BOC}\cong\triangle\text{DOC}$? State the congruence condition used?
$ii.$ Also state, if $\angle\text{BCO}=\angle\text{DCO}$
✓

Answer



$i.$ Yes
In $\triangle\text{BCO}$ and $\triangle\text{DCO}$
$\text{OC}=\text{OC} ($common$)$
$\text{BC}=\text{DC} ($all sides of a rhombus are equal$)$
$\text{BO}=\text{OD} ($diagonals of a rhomus bisect each other$)$
By SSS congruence:
$\triangle\text{BOC}\cong\triangle\text{DOC}$
$ii.$ Yes
By $\text{c.p.c.t}:$
$\angle\text{BCO}=\angle\text{DCO}$

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