Here are the questions:

1.)

In the triangle ABC, let M and N be the midpoints of AB and AC respectively. Show that vector MN is equal to one-half of vector BC. Conclude that the line segment joining the midpoints of two sides of a triangle is parallel to the third side. How are their lengths related?

2.)

Use vectors to prove that the midpoints of the four sides of an arbitrary quadrilateral are the vertices of a parallelogram.

Thanks A Lot