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 $$\triangle\, ABC, D$$ is midpoint of $$AB$$ and $$DE$$ is parallel to $$BC.$$$$\therefore$$ $$AD=DB$$To prove: $$AE = EC$$Proof: Since, $$DE \parallel BC$$$$\therefore$$ By Basic Proportionality Theorem,$$\dfrac{AD}{DB}=\dfrac{AE}{EC}$$Since, $$AD = DB$$$$\therefore$$ $$\dfrac{AE}{EC}=1$$$$\therefore$$ $$AE=EC$$MathematicsRS AgarwalStandard X

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