In figure, \(FG\)\( || \)\(OS\) and \(FH\)\(|| \),show that\(GH\)\(||\)\(ST\).
Proof:
In \(\Delta\)\(RSO\),
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 \(\Delta \)\(RTO\),
\(FH\)\(|| \)
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, \(GH\)\(||\)\(ST\).