Question

In the following figure, ABCD is a trapezium in which AB || DC. E and F are points on AD and BC, respectively, such that EF || CD. Prove that `(AE)/(ED) = (BF)/(FC)`

Answer 1

Since AB || EF || DC, these three parallel lines cut the transversals AD and BC.

By the intercept theorem (or Basic Proportionality Theorem),

`(AE)/(ED) = (BF)/(FC)`

Thus, `(AE)/(ED) = (BF)/(FC)`

Hence proved.