Question

state and prove the mid point theorem

Answer 1

mid point theorem :

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

Given:

A triangleABC in which D and E the midpoints of AB and AC, respectively.

To prove:

DE||BC

Proof:

since D and E are the midpoints of AB and AC, respectively, we have AD=DB and AE=EC.

therefore,

AD/DB=AE/EC ( each equal to 1 )

therefore, by the converse of Thales theorem,DE||BC