Since this is an indirect proof, we always assume the thing that is opposite to what we want to prove is true. Thus: 1. ZW is perpendicular to XY. 2. If ZW is perpendicular to XY, then XYZ is broken into two separate, equal triangles. 3. If there are equal triangles, then two sides of the original triangle XYZ are identical. 4. If two sides are identical to angles are identical. 5. If two angles are identical, then the triangle is not scalene by the definition of a scalene triangle. 6. The triangle is scalene. 7. Thus, this means that the original statement in (1) is false, so ZW is not perpendicular to XY.