Ex.6.2 Q5 Triangles Solution - NCERT Maths Class 10

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In Figure, \(DE || OQ\) and \(DF || OR.\) Show that \(EF || QR.\)

Text Solution



As we know if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.


In \(\Delta P O Q\)

\[\begin{align}D E \;&|| O Q \text { (given) } \\ \frac{P E}{E Q}&=\frac{P D}{O D}.........(1)\end{align}\]

In \(\Delta POR\)

\[\begin{align}& DF||OR\left( \text{given} \right) \\ & \frac{PF}{FR}=\frac{PD}{DO}.........(2) \\ \end{align}\]

From \((1)\)\((2)\)

\[\begin{align} \frac{PE}{EQ}&=\frac{PF}{FR}=\frac{PD}{DO} \\ \frac{PE}{EQ}&=\frac{PF}{FR} \\ \end{align}\]

In \(\Delta PQR\)

\[\begin{align}\frac{PE}{EQ}=\frac{PF}{FR} \end{align}\]

\(\therefore\;\;QR||EF\)  (Converse of \(BPT\))

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