Diagonals AC and BD of a trapezium ABCD with AB || DC, intersect each

1.	Diagonals AC and BD of a trapezium ABCD with AB \|\| DC, intersect each other at ‘O’. Prove that ar.(∆AOD) = ar.(∆BOC).
Answer» Data: Diagonals AC and BD of a trapezium ABCD with AB \|\| DC, intersect each other at ‘O’. To Prove: ar.(∆AOD) = ar.(∆BOC) Proof: ∆ABD and ∆ABC are on base AB and between AB \|\| DC. ∴ ar. (∆ABD) = ar. (∆ABC) Subtracting ar.(∆ABO) on both sides, ar.(∆ABD) – ar.(∆ABO) = ar.(∆ABC) – ar.(∆ABO) ∴ ar.(∆AOD) = ar.(∆BOC).

Diagonals AC and BD of a trapezium ABCD with AB || DC, intersect each other at ‘O’. Prove that ar.(∆AOD) = ar.(∆BOC).

Answer»

Data: Diagonals AC and BD of a trapezium ABCD with AB || DC, intersect each other at ‘O’.

To Prove: ar.(∆AOD) = ar.(∆BOC)

Proof: ∆ABD and ∆ABC are on base AB and between AB || DC.

∴ ar. (∆ABD) = ar. (∆ABC)

Subtracting ar.(∆ABO) on both sides,

ar.(∆ABD) – ar.(∆ABO) = ar.(∆ABC) – ar.(∆ABO)

∴ ar.(∆AOD) = ar.(∆BOC).