Question 8
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.

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Solution

Given, $Δ A B C$ in which D and E are the mid points of AB and AC respectively such that AD=BD and AE=EC.
To Prove that DE || BC
Proof
D is the mid-point of AB (Given)
$∴ A D = D B$
$\Rightarrow \frac{A D}{B D} = 1 . . . (i)$
Also, E is the mid-point of AC (Given)
$∴ A E = E C$
$\Rightarrow \frac{A E}{E C} = 1..... (i i)$
From equation (i) and (ii), we get
$\frac{A D}{B D} = \frac{A E}{E C}$ , hence, DE || BC [By converse of Basic Proportionality Theorem]

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Question 8 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.

Question 8
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.