Ex.6.2 Q4 Triangles Solution - NCERT Maths Class 10

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Question

In Figure, \(DE || AC\) and \(DF || AE.\) Prove that

\[\begin{align}\frac{BF}{FE}=\frac{BE}{EC}\end{align}\]

Text Solution

  

Reasoning:

 As we know 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.

Steps:

In \(\Delta ABC\)

\[\begin{align} & DE||AC \end{align}\]

\[\begin{align}\frac{BD}{AD}=\frac{BE}{EC}\,\,\,.........\rm{(i)} \\ \end{align}\]

In\(\begin{align}\Delta \,ABE \end{align}\)

\[\begin{align}&DF||AE \\ &\frac{BD}{AD}=\frac{BF}{FE}\,\,\,........\rm{(ii)} \end{align}\]

From \(\rm (i)\) and \(\rm (ii)\)

\[\begin{align} & \frac{BD}{AD}=\frac{BE}{EC}=\frac{BF}{FE} \\ & \frac{BE}{EC}=\frac{BF}{FE} \\ \end{align}\]

  
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