prove that a line drawn through the mid point of one side of a triangle parellel to another side bisects the third side
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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.
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