Find a point G along the long edge (AC) such that AG is equal to the length of the smaller square's side (y) and GC is equal to the length of the larger square's side (x). Make your two straight cuts along FG and GD. The triangle AFG can be pivoted around point F to rest above the larger piece. The triangle CDG can be pivoted around point D to rest above the edge DE.

Left-brain thinkers will love the fact that this is just an application of the Pythagorean Theorem. The area of the larger square (x²) + the area of the smaller square (y²) equals the area of the combined square z² (x² + y² = z²). We are creating two identical right triangles (AFG and CDG) where the hypotenuse is the edge of the new, combined square.

Right-brain thinkers can immediately see that the three pieces will fit together to form the new square! This puzzle is much easier than I first thought it was.