Diagonal AC and BD of trapezium ABCD in which $A B | | D C$ , intersect each other at O. The triangle which is equal in area of $Δ$ AOD is:

Δ A O B

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Δ B O C

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Δ D O C

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Δ A O C

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Solution

The correct option is B $Δ B O C$

Diagonals of $A C$ and $B D$ of a trapezium $A B C D$ with $A B ∥ C D$ intersect each other at $O .$
$△ A D B$ and $△ A C B$ are on the same base $A B$ and between the same parallels $A B$ and $D C$
We know, two triangles on the same base and between the same parallels are equal in area.
$∴$ $a r (△ A D B) = a r (△ A C B)$
Subtracting $a r (△ A O B)$ from both sides.
$\Rightarrow$ $a r (△ A D B) - a r (△ A O B) = a r (△ A C B) - a r (△ A O B)$
$∴$ $a r (△ A O D) = a r (△ B O C)$

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