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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)

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Answer:

See Explanation

Step-by-step 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)

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