Question

prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and has length half that of the third side

Answer 1

This is also known as mid-point theorem.
Go here for video lecture:

http://www.youtube.com/watch?v=ozb998JdeDI

Answer 2

Or this
http://www.algebra.com/algebra/homework/Triangles/The-line-segment-joining-the-midpoints-of-two-sides-of-a-triangle.lesson