# 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. (Recall that you have done it in Class IX). - Mathematics

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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. (Recall that you have done it in Class IX).

#### Solution

Given, In ΔABC

D and E are the midpoints of AB and AC respectively, such that,

AD = BD and AE = EC.

We have to prove that: DE || BC.

Since, D is the midpoint of AB

⇒ (AD)/(BD)  = 1  .......(i)

Also given, E is the midpoint of AC.

∴ AE = EC

⇒ (AE)/(EC) = 1

From equation (i) and (ii), we get,

(AD)/(BD) = (AE)/(EC)

By converse of Basic Proportionality Theorem,

DE || BC

Hence, proved.

Concept: Basic Proportionality Theorem (Thales Theorem)
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 6 Triangles
Exercise 6.2 | Q 8 | Page 129

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