Question 7 Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.
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Solution
Given, ΔABC in which D is the mid-point 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 that E is the mid-point of AC.
Proof
D is the mid-point of AB. ∴AD=DB ⇒ADBD=1...(i)
In ΔABC,DE||BC,
Therefore, ADDB=AEEC [By using Basic Proportionality Theorem] ⇒1=AEEC [From equation (i)] ∴AE=EC
Hence, E is the mid-point of AC.