Ex.6.2 Q5 Triangles Solution - NCERT Maths Class 10

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Question

In Figure, $$DE || OQ$$ and $$DF || OR.$$ Show that $$EF || QR.$$

Text Solution

Reasoning:

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.

Steps:

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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