Question
From given information, is PQ || BC?
AP = 2, PB = 4, AQ = 3, QC = 6
AP = 2, PB = 4, AQ = 3, QC = 6
✓
Answer
$\frac{ AP }{ PB }=\frac{2}{4}=\frac{1}{2}$
...(i)[Given]
$\frac{ AQ }{ QC }=\frac{3}{6}=\frac{1}{2}$
In $\triangle A B C$,
$\frac{ AP }{ PB }=\frac{ AQ }{ QC }=\frac{1}{2}$
.[From (i) and (ii)]
$\therefore$ Line $PQ \|$ side $BC$
.[Converse of basic proportionality theorem]
...(i)[Given]
$\frac{ AQ }{ QC }=\frac{3}{6}=\frac{1}{2}$
In $\triangle A B C$,
$\frac{ AP }{ PB }=\frac{ AQ }{ QC }=\frac{1}{2}$
.[From (i) and (ii)]
$\therefore$ Line $PQ \|$ side $BC$
.[Converse of basic proportionality theorem]
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