Fill in the blanks: We know that angle WZX is congruent to angle YZX and that sides ZW is congruent to side ZY. The property allows us to say that line segment ZX is congruent to itself. Thus by the congruency theorem, ΔWZX ≅ ΔYZX. We know that Corresponding Parts of Congruent Triangles are , so ∠ZXY ≅ ∠ZXW. Because they make up the straight line segment WY, the two angles are a

, which means that m∠ZXY + m∠ZXW =

°. Because the angles are equal, we can use substitution to get 2(m∠ZXW) = 180°. Solving, we find that both angles equal 90°. This implies that line segment ZX is to WY by the definition of perpendicular. Finally, using CPCTC again we know that WX ≅ YX. Therefore, X is the of WY, and ZX is the of WY.