Question

Fig. 9.26
10. Diagonals AC and BD of a trapezium ABCD with AB DC intersect each other so
Prove that ar (AOD) = ar (BOC).​

Answer 1

Answer:

Two Triangles on the same base and between the same parallels are equal in area. Given: Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. To Prove: ar (AOD) = ar (BOC).

Step-by-step explanation:

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Answer 2

Dear user:

Given:

AB||DC

TO PROVE:

ar(AOD) =ar(BOC)

Proof

ΔADC and ΔBDC are on the same base DC and between same parallel AB and DC.

∴ ar(ΔADC) = ar(ΔBDC) [triangles on the same base and between same parallel are equal in area]

Subtract Area (ΔDOC) from both side.

ar(ΔADC) – ar(ΔDOC) = ar(ΔBDC) – ar(ΔDOC)

ar(ΔAOD) = ar(ΔBOC)

Hence proved☺☺

#AN