Question

Diagonals AC and BD of a trapezium ABCD with AB||DC intersect each other at O. Prove that diagonals of a rectangle is equal​

Answer 1

Using Theorem:-

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 thesame 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...!!