Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ . Use the drop-down menus to complete the proof of the Pythagorean theorem. By the angle-angle similarity postulate, △YXZ∼△YZQ and △YXZ∼△ZXQ. Since similar triangles have sides, ac=fa and bc=eb . Solving the equation for a² and b² gives a2=cf and b2= . Adding these together gives a2+b2=cf+ce. Factoring out the common segment gives a2+b2=c(f+e). Using gives a2+b2=c(c), which simplifies to a2+b2=c2 .