# Ex.6.2 Q7 Triangles Solution - NCERT Maths Class 10

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## Question

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 $$AC.$$

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