Question

abcd is a trapezium. diagonals ac and bd intersect each other at o. find the ratio ar(triangle AOD) :ar(triangle BOC).

Answer 1

Given: AB||CD.
To find: ar(AOD):ar(BOC)=?
Procedure: Triangles ADC and BDC are on same base DC and between same parallels AB||DC.
ar(ADC)=ar(BDC)
By subtracting ar(COD) on both sides, 
ar(AOD)=ar(BOC)_____(i)
ar(AOD):ar(BOC)=1:1    [From (i)]