Question

ABCD is a trapezium such that AB is parallel to DC . The AC and BD intersect each other at O. Prove that AO.DO=BO.CO

Answer 1

Step-by-step explanation:

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Answer 2

dear Friend

Given

ABCD is a trapezium

AB || DC and Diagonal AC

BD intersect each other at O.

To prove:

Area (AOD) = Area (BOC)

Proof:

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

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

Subtract Area (ΔDOC) from both side

Area (ΔADC) – Area (ΔDOC) = Area (ΔBDC) – Area (ΔDOC)

Area (ΔAOD) = Area (ΔBOC)

Hence proved.

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