Question

State and prove mid point theorem.

Answer 1

Mid point Theorem :

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

Given :

A $△ABC$ in which D and E are the mid points of AB and AC, respectively.

To prove :

$DE\parallel BC$.

Proof :

Since D and E are the mid points of AB and AC, respectively, we have $AD=DB$ and $AE=EC$.

Therefore,

$\frac{AD}{DB}=\frac{AE}{EC}$ ( each equal to 1 )

Therefore, by the converse of thales theorem, $DE\parallel BC$.