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Two Triangles Having the Same Base & Equal Areas

Question 10Di...

Question

Question 10
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

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Solution

It can be observed that $Δ D A C$ and $Δ D B C$ are on the same base DC and between same parallel AB and DC.
$∴ A r e a (Δ D A C) = A r e a (Δ D B C)$
Then, $A r e a (Δ D A C) - A r e a (Δ D O C) = A r e a (Δ D B C) - A r e a (Δ D O C)$
[Subtracting Area $(Δ D O C)$ from both sides]
$\Rightarrow A r e a (Δ A O D) = A r e a (Δ B O C)$

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Diagonals AC and BD of a trapezium ABCD with AB $∥$ DC intersect each other at O.
Prove that ar ( $△$ AOD) = ar ( $△$ BOC). [1 MARK]

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