Question

.   AB and CD are parallel sides of trapezium ABCD. Diagonals AC and BD intersect at O. prove that ar(ΔAOD) = ar(ΔBOC).

Answer 1

◀ Method of Solution: ◀

Given:→ ABCD is a trapezium with AB || DC and Diagonal AC and BD intersect each other at O.

To prove:  

→ Ar (AOD) = Ar(BOC)

Proof: 

→ In ∆ADC and ∆BDC,

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

→ We know that triangles on the same base and between same parallel are equal in area: →

Therefore,

∴Area (ΔADC) = Area (ΔBDC)   

Subtracting ar(ΔDOC) from LHS and RHS(Both Sides)

Thus, We gets

Ar(ΔADC) – Ar (ΔDOC) = Ar (ΔBDC) – Ar(ΔDOC)

Area (ΔAOD) = Area (ΔBOC)

◀  PROVED