In the given figure, if \(GE||CB\) and \(GF||CD\), prove that \(\frac{AE}{AB} = \frac{AF}{AD}\).
Proof:
In \(\Delta ACB\),
\(GE || CB\)
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
\(\frac{AG}{GC} =\) - - - - (1)
In \(\Delta ACD\),
\(GF || CD\)
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
\(\frac{AG}{GC} =\) - - - - (2)
From (1) and (2),
\(\frac{AE}{EB} = \)
\(\frac{EB}{AE} = \)
Adding \(1\) on both sides, we get
\(\frac{AE}{AB} = \frac{AF}{AD}\)
Hence proved.