In the given figure, \(DE||OQ\) and \(DF||OR\), prove that \(EF || QR\).
Proof:
In \(\Delta PQO\),
\(DE ||\)
\(\frac{PE}{EQ} = \frac{PD}{DO}\) - - - - (1)
In \(\Delta PRO\),
\(DF ||\)
\(\frac{PF}{FR} = \frac{PD}{DO}\) - - - - (2)
From (1) and (2),
\(\frac{PF}{FR} = \frac{PE}{EQ}\)
In \(\Delta PQR\),
\(\frac{PF}{FR} =\)
Thus, \(EF||QR\).
Answer variants:
\(\frac{PE}{EQ}\)
\(OR\)
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.
\(\frac{PO}{OQ}\)
If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side
\(OQ\)