Pythagorean Theorem Water Areas Proof

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Point(xAxis) → B
3. Semicircle(A, B) → c
4. Point(c) → C
5. Polygon(A, C, B) → t1, b, a, c_1
6. Polygon(A, C, 4) → poly1, f, g, h, i, D, E
7. Polygon(C, B, 4) → poly2, j, k, l, m, F, G
8. Polygon(B, A, 4) → poly3, n, p, q, r, H, I
9. Line((0, 0), (1, 0)) → s
10. Rotate(poly1, aa, J) → poly1'
11. Rotate(E, aa, J) → E'
12. Rotate(D, aa, J) → D'
13. Rotate(A, aa, J) → A'
14. Rotate(C, aa, J) → C'
15. Rotate(poly2, aa, J) → poly2'
16. Rotate(B, aa, J) → B'
17. Rotate(F, aa, J) → F'
18. Rotate(G, aa, J) → G'
19. Rotate(poly3, aa, J) → poly3'
20. Rotate(I, aa, J) → I'
21. Rotate(H, aa, J) → H'
22. Rotate(A, aa, J) → A'_1
23. Rotate(C, aa, J) → C'_1
24. Rotate(B, aa, J) → B'_1
25. Polygon(A'_1, C'_1, B'_1) → t1', b'_1, a'_1, c'_1
26. Intersect(s, poly1') → K, L
27. Intersect(s, poly3') → M, N
28. Intersect(s, poly2') → O, O_1
29. Angle(C, B, A) → α
30. Polygon(H', A', J, N, I') → poly4, h', a', j_1, n_1, i'
31. Polygon(A', J, N) → t2, n_2, t, j_2
32. Polygon(A', E', D', K, L) → poly5, d, e', d', k_1, l_1
33. Polygon(K, A', L) → t3, l_2, k_2, e
34. Polygon(E', D', C', A') → q1, f_1, g_1, c', h_1
35. Polygon(C', G', F', O, O_1) → poly6, i_1, g', f', o, o_1
36. Polygon(C', O, O_1) → t4, m_1, p_1, o_2
37. Polygon(F', B', C', G') → q2, q_1, b', r_1, s_1
38. Angle(B', C', A') → β