Question

In the given figure, if ABCD is a trapezium in which AB | | CD | | EF, then prove that AE/ED = BF/FC

Answer 1

Answer:

Construction join ac and meets ef at g

Step-by-step explanation:

In triangle adc

Ae/ed=Ag/gc By Basic prop. Theo. 1

In triangle abc

bf/fc=Ag/gc. By BPT.... 2

:. By 1&2

Ae/ed=bf/fc

Answer 2

In triangle ADC,
EF||DC
Thus
AE/ED = AM/MC - (1) (basic proportionality theorem)

Similarly,
In triangle BAC

BF/FC = AM/MC - (2) ( bpt theorem)

From eq 1 and 2,
AE/ED = BF/FC

hence proved