In the given figure, \(EF\)\( || \)\(OR\) and \(EG\)\(|| \),show that\(FG\)\(||\)\(RS\).
Proof:
In \(\Delta\)\(QRO\),
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.
- - - (1)
In \(\Delta \)\(QSO\),
\(EG\)\(|| \)
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.
- - - (2)
From (1) and (2),
In \(\Delta \),
If a line divides any two sides of a triangle in the same ratio, then the line is to the third side.
Thus, \(FG\)\(||\)\(RS\).