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In the given ...

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Question 4
In the given figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar(ABC) = ar(ABD).

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Solution

Consider $Δ A C D$ .
Line-segment CD is bisected by AB at O. Therefore, AO is the median of $Δ A C D$ . $∴ A r e a (Δ A C O) = A r e a (Δ A D O) . . . (1)$
Considering $Δ B C D, B O$ is the median.
$∴ A r e a (Δ B C O) = A r e a (Δ B D O) . . . (2)$
Adding equations(1) and (2), we obtain;
$A r e a (Δ A C O) + A r e a (Δ B C O) = A r e a (Δ A D O) + A r e a (Δ B D O)$
$\Rightarrow A r e a (Δ A B C) = A r e a (Δ A B D)$

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Standard IX Mathematics