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