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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02-07-2021
Mathematics

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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)

Sagot :

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virtuematane virtuematane · Answer 1 · 2021-07-07T23:22:39-04:00

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)

Sagot :

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