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Understanding Shapes - II (Special Types of Quadrilaterals) — Maths STD 8 — Question

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

Answer


  1. 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:

$\triangle\text{BOC}\cong\triangle\text{DOC}$
  1. Yes
By c.p.c.t:

$\angle\text{BCO}=\angle\text{DCO}$

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