1)
The vectors and are colinear, then
2) Use the first problem in the triangles formed by three vertices of the parallelogram.
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
Let ABCD be the parallelogram, M the midoint of AB, N the midoint of BC, P the midoint of CD, Q the midpoint of DA.
Use the problem 1 in the triangle ABC with the points M, N, then in the triangle CDA with the points P, Q.
You'll get that MN and PQ are parallel to AC and their length is half of AC. So MNPQ is a parallelogram.