Question

state and prove midpoint theorem​

Answer 1

Answer:

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Explanation:

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∥BC.

Proof :

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

Therefore,

DB =EC ( each equal to 1 )

AD AE

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