Question

Using converse of thales theorem,prove that the line joining the mid points of any two sides of a triangle is parallel to the third side

Answer 1

$\bf\huge\underline{Question}$

Using converse of thales theorem,prove that the line joining the mid points of any two sides of a triangle is parallel to the third side

$\bf\huge\underline{Answer}$

We have ∆ABC in which D and E are the mid-points of sides AB and AC respectively.

Therefore, AD = DB ⠀⠀⠀⠀⠀⠀⠀⠀⠀.....(1)

and AE = EC ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ .....(2)

From (1) and (2), we have

$\dfrac{AD}{DB}$ = 1 and $\dfrac{AE}{EC}$ = 1

=> $\dfrac{AD}{DB}$ = $\dfrac{AE}{EC}$

=> DE || BC (By converse of Basic proportionality theorem).