Answer
The proof is in the following form:
Column 1 of proof; Column 2 of proof.
Thus, we have:
1. WX is congruent to WZ, and YW bisects angle XYZ; given
2. $\frac{YX}{YZ} = \frac{WX}{WZ}$; angle bisector theorem
3.$ \frac{WX}{WZ}=1$; when two equal lengths are divided, the result is one.
4. $\frac{YX}{YZ} = 1$; substitution
5. YX is congruent to YZ; simplification of (4), and line segments with the same length are congruent.
6. XYZ is isosceles; by definition, if the sides are equal in length, the triangle is isosceles.
