In the figure, line
\(
DE\) is drawn parallel to
\(
OQ\) and line
\(
DF\) is drawn parallel to
\(OR\). Prove that the segment
\(EF\) is parallel to
\(
QR\).
Proof:
In \(\Delta PQO\),
\(DE ||\)
\(\frac{PD}{DO}=\) - - - - (1)
In \(\Delta PRO\),
\(DF ||\)
By
\(\frac{PD}{DO}=\) - - - - (2)
From (1) and (2),
\(\frac{PF}{FR} =\)
In \(\Delta PQR\),
\(\frac{PF}{FR} =\)
By
Thus, \(EF||QR\).
Answer variants:
\(\frac{PE}{FR}\)
\(\frac{PE}{EQ}\)
\(OR\)
\(OQ\)
\(\frac{PF}{FR}\)