Use a paragraph, flow chart, or two-column proof to prove that is the perpendicular bisector of side . given: wzx yzx; prove: is a perpendicular bisector of [see image]

The data given 
∠wzx =  ∠yzx   given
wz = zy             given
zx = zx               this is common for both triangles
2 sides and angle between the 2 sides are congruent to the 2 sides and angle in the other triangle. according to side angle side (sas) congruency theorem;
δwzx  ≡δyzx
this means that all three sides and all three angles are congruent to three sides and three angles of the other triangle.
then  ∠wxz =  ∠yxz and wx = xy
lets name one angle as x
since both angles are equal , both are x
x + x = 180°
x = 90°
therefore zx cuts wy at x making 2 right angles and cuts wy at the midpoint of wy. therefore zx is the perpendicular bisector of wy