Question

Given the following diagram how would I determine whether quadrilateral XYZW must be parallelogram and justify line XN is congruent to YN and WN is congruent to ZN

Answer 1

if you are also given that
XY is parallel to WZ
and XW is parallel to YZ
then
XYZW is a parallelogram

Answer 2

if it is a parallelogram then the diagonals intersect each other

Answer 3

This is theorem 6.9

Answer 4

Just checking to see if I am on the right track?