In the given figure, \(PQ||XZ\) and \(PR||XQ\), prove that \(\frac{YR}{RQ} = \frac{YQ}{QZ}\).
Proof:
In \(\Delta XYZ\),
\(PQ ||\)
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.
\(\frac{YQ}{QZ} =\) - - - - (1)
In \(\Delta XQY\),
\(PR ||\)
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.
\(\frac{YR}{RQ} =\) - - - - (2)
From (1) and (2) we get,
Hence proved.