Question

Using B.P.T., 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 your have proved it in class IX)

Answer 1

See Explanation

Explanation:

(For Diagram please find in attachment)

• Given, Let Assume triangle ABC Where, DE is Parallel to BC & D is midpoint to AB . ∵ AD=DB

• To Prove, E is the midpoint of AC.

• Proof, 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.

Since DE∥BC

∴ By Basic Proportionality Theorem,

AD/DB = AE/EC

​ Since it is Given, AD=DB

∴ AE/EC =1

∴ AE=EC (Proved)