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Question:

Using Theorem 6.1, 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). Theorem 6.1: 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.

Solution:

Given: In △ABC, D is midpoint of AB and DE is parallel to BC. ∴ AD = DB
To prove: AE = EC
Proof: Since, DE∥BC
∴ By Basic Proportionality Theorem, AD/DB = AE/EC
Since, AD = DB
∴ AE/EC = 1
∴ AE = EC