Question 675434
Since X is the midpoint, you know WX=XY  and VX=XZ (given to you in the problem statement)

When you draw your line segments, label the five points W,X,Y,V and Z

Now also draw line segments WV and ZY. 
You now have two triangles.
The angle zxy = wxv since opposite angles are equal.
Given the above, you now have 2 triangles that are congruent using side-angle-side

Since the two triangles are congruent, then the sides opposite the angle x (WV and ZY) must be equal.

Write that down as a series of steps and you have your proof!