Question

In analyzing this diagram, which statement represents a crucial step to proving the Pythagorean theorem using this diagram?

Answer 1

Pythagorean theorem establishes that the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

So, according to the figure above the two large squares each contain four identical triangles (two purples and two pinks: those are congruent triangles). Therefore the area of the blue space equals the sum of the green area and the yellow area.