Points
\(A\),
\(B\), and
\(C\) are located on \(OP\), \(OQ\) and \(OR\). Given that
\(AB||PQ\) and \(AC||PR\). Demonstrate that the segment
\(
BC\) must be parallel to
\(QR
\).
Proof:
We know that, 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.
In \(\Delta OPQ\),
\(AB ||\)
\(\frac{OA}{AP} = \) - - - - (1)
And also in \(\Delta OPR\),
\(AC ||\)
\(\frac{OC}{CR} = \) - - - - (2)
From (1) and (2),
\(\frac{OC}{CR} =\)
In \(\Delta OQR\),
\(\frac{OC}{CR} = \frac{OB}{BQ}\)
By theorem,
Thus, \(BC||QR\).
Answer variants:
\(PQ\)
\(PR\)
\(\frac{OB}{BQ}\)
\(\frac{OA}{AP}\)