The Pythagorean Theorem - Educational Outreach

Notice that the right-triangle property implies that the sumof the two acute interior angles equals the right angle asproved below. 180 900 900 0&Thus, for any right triangle, the sum of the two acute angles0equals the remaining right angle or 90 ; eloquently statedin terms of Figure 1.5 as .Continuing our exploration, let’s replicate thegeneral right triangle in Figure 1.5 eight times, dropping allalgebraic annotations. Two triangles will then be fusedtogether in order to form a rectangle, which is shaded viathe same shading scheme in Figure 1.4. Figure 1.6 showsthe result, four bi-shaded rectangles mimicking the four bishadedsquares in Figure 1.4.Figure 1.6: Four Bi-Shaded Congruent RectanglesWith our new playing pieces, we rotate as before, finallyarriving at the pattern shown in Figure 1.7.21