1. TWX is isosceles--given. 2. The angles of the bases of isosceles triangles are congruent, so X and W are congruent. 3. RY and WX are parallel. 4. Thus, angle W and angle WRY are supplementary, and angle X and angle XYR are supplementary. 5. Since it is a four-sided shape with opposite angles being supplementary and corresponding angles being congruent, it is a trapezoid.