Question

How to prove mid point theorem

Answer 1

triangle midpoint theorem :- the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and congruent to one half of the third side . here"s the proof below

Answer 2

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

To prove :

DE \parallel BCDE∥BC.

Proof :

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

Therefore,

\dfrac{AD}{DB}=\dfrac{AE}{EC}  

DB

AD

​  

=  

EC

AE

​  

           ( each equal to 1 )

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