Question

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Question 7. Using theorem, prove that a line drawn through the
mid-point of one side of a triangle parallel to another side bisects the
third side. (recall that you have proved it in Class IX).
Solution In A ABC. Dis the mid-noint of AR​

Answer 1

Step-by-step explanation:

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Answer 2

Given,In triangle ABC, D is the midpoint of AB such that AD=DB.

A line parallel to BC intersects AC at E as shown in above figure such that DE||BC.

To prove, E is the midpoint of AC.

Since, D is the midpoint of AB

So,AD=DB

⇒ AD/DB=1.....................(i)

In triangle ABC,DE||BC,

By using basic proportionality theorem,

Therefore, AD/DB=AE/EC

From equation 1,we can write,

⇒ 1=AE/EC

So,AE=EC

Hence, proved,E is the midpoint of AC.