MathPlotAI Logo MathPlotAI

Pythagorean Theorem Proof with Diagram

Pythagorean Theorem Proof with Diagram
Loading the math board and drawing, please wait…
2020-04-12 03:54
TrianglePolygonCoordinate Geometry
Calculate the area of the red square in two ways to indirectly prove the Pythagorean Theorem. This example involves squares, right triangles, and geometric construction. It uses Segment, OrthogonalLine, Circle, Intersect, Point, Polygon, Angle, etc., GeoGebra commands. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Circle(A, B) → c
  5. Circle(B, A) → d
  6. Intersect(d, h, 2) → C
  7. Intersect(c, g, 2) → D
  8. Segment(C, D) → i
  9. Segment(D, A) → j
  10. Segment(B, C) → k
  11. Point(j) → E
  12. Circle(A, E) → e
  13. Circle(B, Radius[e]) → p
  14. Circle(C, Radius[p]) → q
  15. Circle(D, Radius[q]) → r
  16. Intersect(r, i, 1) → F
  17. Segment(E, F) → l
  18. Intersect(q, k, 1) → G
  19. Segment(F, G) → m
  20. Intersect(p, f, 1) → H
  21. Segment(G, H) → n
  22. Segment(H, E) → s
  23. Polygon(E, F, G, H) → q1, e_1, f_1, g_1, h_1
  24. Polygon(A, H, E) → t1, e_2, a, h_2
  25. Polygon(E, D, F) → t2, f_2, e_3, d_1
  26. Polygon(F, G, C) → t3, c_1, f_3, g_2
  27. Polygon(H, B, G) → t4, g_3, h_3, b
  28. Point(t4) → I
  29. Point(t3) → J
  30. Point(t4) → K
  31. Angle(B, A, D) → α
  32. Angle(A, D, C) → β
  33. Angle(D, C, B) → γ
  34. Angle(C, B, A) → δ
  35. Angle(E, H, G) → ε
  36. Angle(H, G, F) → ζ
  37. Angle(G, F, E) → η
  38. Angle(F, E, H) → θ