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

##### Solution :-

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

We have to prove that: DE || BC.

Since, D is the midpoint of AB

$$\dfrac{AD}{BD}$$ = 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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