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# In the figure $\vartriangle ABC$ and $\vartriangle ABD$ are two triangles on the same base AB. If line segment CD is bisected by AB at O. Show that $area\left( {\vartriangle ABC} \right) = area\left( {\vartriangle ABD} \right)$

Last updated date: 15th Mar 2023
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Hint: Here we apply the area of triangle theorem where median divides the triangle in two equal areas.

In $\vartriangle ABC$
So,$area\left( {\vartriangle AOC} \right) = area\left( {\vartriangle AOD} \right)$ …… (1)
Also, in $\vartriangle BCD$
So, $area\left( {\vartriangle BOC} \right) = area\left( {\vartriangle BOD} \right)$ …… (2)
$area\left( {\vartriangle AOC} \right) + area\left( {\vartriangle BOC} \right) = area\left( {\vartriangle AOD} \right) = area\left( {\vartriangle BOD} \right)$
$\Rightarrow area\left( {\vartriangle ABC} \right) = area\left( {\vartriangle ABD} \right)$