Question

In the below fig. ABCD is a trapezium in which AB || DC. Prove that ar (ΔAOD) =
ar(ΔBOC).

Answer 1

Given: ABCD is a trapezium with  AB ||DC
To prove: ar (ΔAOD) = ar (BOC)
Proof:

Since ΔADC and ΔBDC are on the same base DC and between same parallels AB and DC
Then, ar (ΔADC )  = ar (ΔBDC)

⇒ ar (ΔAOD) + ar ( DOC) = ar (ΔBOC) + ar ( ΔDOC) 

⇒ ar (ΔAOD) = ar (ΔBOC)