Ex.6.2 Q7 Triangles Solution - NCERT Maths Class 10


Using Theorem \(6.1\), prove that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

 Video Solution
Ex 6.2 | Question 7

Text Solution


We know that theorem \(6.1\) states 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 (\(BPT\))”.


In \(\Delta ABC\)\(, D\) is the midpoint of \(AB\)


\[AD = BD\]

\[ \frac{AD}{BD}=1\]


\[\begin{align}DE&||BC \\ \Rightarrow\frac{AE}{EC}&=\frac{AD}{BD}\,\,\,\text{[Theorem} \,6.1] \\ \Rightarrow \frac{AE}{EC}&=1 \end{align}\]

Hence \(,E\) is the midpoint of \(AC.\)

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