Question

In the figure, diagonals AC and BD of a trapezium ABCD with AB||DC intersect each other at O. Prove that ar(ΔAOD) = ar(ΔBOC).

Answer 1

Answer:

Area of ΔAOD = Area of ΔBOC

ar(ΔAOD) = ar(ΔBOC)

Step-by-step explanation:

lets draw DM ⊥ BC   & CN ⊥ BC

as AB ║ DC

=> DM ║ CN

=> DM = CN

Area of ΔABD = (1/2) AB * DM

Area of ΔABC = (1/2) AB * CN

DM = CN

=> Area of ΔABC = (1/2) AB * DM

=> Area of ΔABD = Area of ΔABC

Area of ΔABD  = Area of ΔAOD + Area of ΔAOB

Area of ΔABC = Area of ΔBOC + Area of ΔAOB

=> Area of ΔAOD + Area of ΔAOB = Area of ΔBOC + Area of ΔAOB

cancelling Area of ΔAOB from both sides

=> Area of ΔAOD = Area of ΔBOC

ar(ΔAOD) = ar(ΔBOC)