Question

if ABCD is a trapezium in which AB || CD || EF then prove that AE/ED is equals to BF/FC

Answer 1

Let EF and AC intersect at O
THEN ADC IS TRIANGLE WITH BASE DC , EOllDC
THEN BY BASIC PROPORTIONALITY THEOREM, AE/ED=AO/OC ----.(1)

ABC IS A TRIANGLE WITH BASE AB , FOllAB
THEN BY BASIC PROPORTIONALITY THEOREM, BF/FC=AO/OC ----(2)

FROM (1)AND(2),

AE/ED=BF/FC

HENCE,PROVED