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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)`
Sum
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Solution
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.
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