Question

(19) Geometry pls help

Answer 1

Yes it is possible to prove this is a parallelogram.

XN = NZ means the diagonal XZ has been bisected
The same goes for diagonal WY (because NY = NW)

Furthermore, we have the pair of vertical angles XNY and ZNW which are congruent

Through SAS, we can say that triangles XNY and ZNW are congruent

Using CPCTC, we can get to the fact that angle NWZ = angle NYX which are alternate interior angles leading to proving that XY || WZ

----------------------

If you repeat those steps above, but focus on triangles WNX and YNZ, we can prove that XW || YZ

----------------------

After proving that XY || WZ and XW || YZ, this is enough to prove we have a parallelogram as the opposite sides are parallel.