Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

 

Asked by Pragya Singh | 1 year ago |  49

1 Answer

Solution :-

Given, in ΔABC, D and E are the mid points of AB and AC respectively, such that,

AD=BD and AE=EC.

Ncert solutions class 10 chapter 6-11

We have to prove that: DE || BC.

Since, D is the midpoint of AB

AD=DB

\( \dfrac{AD}{BD}\) = 1……………………………….. (i)

Also given, E is the mid-point of AC.

AE=EC

⇒ \( \dfrac{AE}{EC}\) = 1

From equation (i) and (ii), we get,

\( \dfrac{AD}{BD}\) = \( \dfrac{AE}{EC}\)

By converse of Basic Proportionality Theorem,

DE || BC

Hence, proved.

Answered by Abhisek | 1 year ago

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