In the given figure, \(HI\)\( || \)\(OU\) and \(HJ\)\(|| \),show that\(IJ\)\(||\)\(UV\).
Proof:
In \(\Delta\)\(TUO\),
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 \(\Delta \)\(TVO\),
\(HJ\)\(|| \)
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.
Therefore, \(IJ\)\(||\)\(UV\).