Yesterday I took a look at some of my old high school notes and stubmled upon this problem. Now, I did not manage to solve it then... and apparently the same is true today so I'm hoping for a clousre.

Let ABCD be a convex polygon (i.e. a polygon containing all its line segments) and let M, N, P and Q be the midpoints of AB, BC, CD and DA.

1. The diagonals MP and NQ intersect at some point R. Show: MR=PR and NR=QR.

2. Form the diagonals in ABCD and let S be the midpoint of AC and T be the midpoint of BD.
a) Show that the polygon QSNT is a parallelogram.
b) What can be said about the polygon MNPT? Prove your statement.
c) What can be said about the points R, S and T? Prove your statement.

Thank you! Any help is more than welcome.