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).

Text Solution

Reasoning:

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 (\(BPT\))”.

Steps:

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

Therefore,

\[AD = BD\]

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

Now,

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

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