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Areas of Parallelograms and Triangles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsAreas of Parallelograms and Triangles2 Marks
Question
In the adjoining figure, ABC and ABD are two triangles on the same base AB. If line segment CD is
bisected by AB at O, show that $\text{ar}(\triangle\text{ABC})=\text{ar}(\triangle\text{ABD}).$
✓

Answer

We know that median of a triangle divides it into two triangles of equal area. Now, AO is the median of $\triangle\text{ACD}.$$\Rightarrow\ \text{A}(\triangle\text{COA})=\text{A}(\triangle\text{DOA})\dots(1)$
And, Bo is the median of $\triangle\text{BCD}.$$\Rightarrow\ \text{A}(\triangle\text{COB})=\text{A}(\triangle\text{DOB})\dots(2)$
Adding (1) and (2), we get:$\text{A}(\triangle\text{COA})+\text{A}(\triangle\text{COB})=\text{A}(\triangle\text{DOA})+\text{A}(\triangle\text{DOB})$
$\Rightarrow\ \text{A}(\triangle\text{ABC})=\text{A}(\triangle\text{ABD})$

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