MathPlotAI Logo MathPlotAI

Pythagorean Theorem Proof by milanofff

Pythagorean Theorem Proof by milanofff
Loading the math board and drawing, please wait…
2012-07-22 18:01
TriangleCoordinate GeometryGeometric Construction
This example demonstrates a geometric proof of the Pythagorean theorem. It involves core mathematical concepts such as right triangles, area, congruent triangles, and parallelograms. The construction utilizes GeoGebra commands like Midpoint, Polygon, Segment, Intersect, Rotate, Line, OrthogonalLine, Distance, Circle, Vector, and Translate to build the geometric figures. It is suitable for middle school and above students to learn and understand the proof process and geometric properties of the Pythagorean theorem.

GeoGebra Commands & Parameters

  1. Midpoint(B, A) → M
  2. Polygon(A, B, 4) → square, bsq, asq, csq, dsq, C_1, D
  3. Segment(A, C_1) → d_1
  4. Segment(B, D) → d_2
  5. Intersect(d_1, d_2) → O
  6. Rotate(A, rot°, M) → C
  7. Polygon(A, C, B) → brown, b, a, b_1
  8. Line(C, B) → m
  9. OrthogonalLine(Z, m) → n
  10. OrthogonalLine(Y, m) → p
  11. Intersect(m, n) → N
  12. Intersect(m, p) → P
  13. Distance(N, P) → r
  14. Circle(B, If[r1 > 0, 0, (-r1) / 40]) → cred
  15. Circle(B, If[r1 > 0, 0, (-r1) / 20]) → cblue
  16. Intersect(cred, m, 1) → BR
  17. Intersect(cred, m, 2) → BG
  18. Intersect(cblue, m, 2) → BB
  19. Vector(B, C) → u
  20. Vector(B, A) → v
  21. Translate(BR, u) → B_1R
  22. Translate(BR, v) → AR
  23. Polygon(AR, B_1R, BR) → red, br, ar, b_1r
  24. Translate(BG, u) → B_1G
  25. Translate(BG, v) → AG
  26. Translate(BB, u) → B_1B
  27. Translate(BB, v) → AB
  28. Rotate(A, If[r1 ≤ 0, 0*°, (3 * r1 / 4)°], O) → A1
  29. Rotate(C, If[r1 ≤ 0, 0*°, (3 * r1 / 4)°], O) → E
  30. Rotate(B, If[r1 ≤ 0, 0*°, (3 * r1 / 4)°], O) → B1
  31. Polygon(A1, E, B1) → red1, b1, a1, b1_1
  32. Rotate(A, If[r1 ≤ 0, 0*°, (r1 / 2)°], O) → A2
  33. Rotate(B, If[r1 ≤ 0, 0*°, (r1 / 2)°], O) → B2
  34. Rotate(A, If[r1 ≤ 0, 0*°, (r1 / 4)°], O) → A3
  35. Rotate(B, If[r1 ≤ 1, 0*°, (r1 / 4)°], O) → B3
  36. Angle(BR, B_1R, AR) → α
  37. Angle(B, C, A) → β
  38. Angle(B1, E, A1) → γ
  39. Polygon(A, B, D) → poly1, d, a_1, b_2