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Constructions
Question
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In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar(Δ AOD) = ar(Δ BOC).

Answer

Given: Diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O.
To Prove: ar(ΔAOD) = ar(ΔBOC)
Proof: ∵ ΔADB and ΔACB are on the same base AB and between the same parallels AB and DC ∴ ar(ΔADB) = ar(ΔACB)
∵ Two triangles on the same base and between the same parallels are equal in area ⇒ ar(ΔADB) – ar(ΔAOB)
= ar(ΔACB) – ar(ΔAOB)
| Subtracting ar(ΔAOB) from both sides Δ ar(ΔAOD) = ar(ΔBOC)

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Some More Questions From Constructions Chapter

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In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar(Δ AOD) = ar(Δ BOC).

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