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).

Class 9 - Math - Areas of Parallelograms and Triangles Page 163"

Answer 1

Two Triangles on the same base and between the same parallels are equal in area.

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Given: Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. 

 

To Prove:

ar (AOD) = ar (BOC).

Proof:

Here,△DAC and △DBC lie on the same base DC and between the same parallels AB and CD.

∴ ar(△DAC) = ar(△DBC)

 ar(△DAC) − ar(△DOC) =ar(△DBC) − ar(△DOC)

 

[On subtracting ar(△DOC) from both sides]

ar(△AOD) = ar(△BOC)

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Hope this will help you...

 

Answer 2

Hi friend ⛎⛎✨✨✨


DIAGONALS AC AND BD OF A TRAPEZIUM -ABCD WITH AB || DC INTERECT EACH OTHER AT O.

∆S ABC AND ABD ARE ON THE SAME BASE AMD BETWEEN THE SAME PARALLELS .

AR(ABD)=AR (ABC)

=AR(ABD)-AR(AOB)=AR(ABC)- AR(AOB)

AR (AOD)=AR(BOC)

thankyou.