Any line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.

GIVEN A trapezium ABCD in which DCI AB and EF is a line parallel to DC and AB. TO PROVE AE/ED = BF/FC

CONSTRUCTION Join AC, meeting EF in G.

PROOF In Δ ADC, we have

EG || DC

AE/ED = AG/GC

IN Δ ABC, we have

GF || AB

AG/GC = BF/FC

From equations (i) and (ii), we get

AE/ED = BF/FC