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Proof of Pythagoras Theorem by Dan

Proof of Pythagoras Theorem by Dan
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2013-02-04 22:49
TriangleCoordinate GeometryGeometric Construction
In collections Right Angled Triangles
This example demonstrates the proof of the Pythagorean Theorem in right triangles. It involves core mathematical concepts such as right triangles, side length relationships, polygon construction, centroids, midpoints, and rotations. The construction uses GeoGebra commands like Intersect, Point, Polygon, Centroid, OrthogonalLine, Line, Rotate, and Midpoint. Suitable for high school mathematics teaching or student exploration of geometric proofs.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Point(a) → Move
  5. Centroid(poly1) → F
  6. Polygon(E, Move, A) → poly2, a_1, e, g
  7. Polygon(Move, H, B) → poly3, b_1, g_1, h
  8. Polygon(H, I, C) → poly4, c_1, h_1, i
  9. Polygon(I, E, D) → poly5, d_1, i_1, e_1
  10. Polygon(I, E, Move, H) → poly6, i_2, e_2, g_2, h_2
  11. Point(xAxis) → J
  12. Point(xAxis) → K
  13. Polygon(G, J, K, L) → poly7, g_3, j, k, l
  14. Polygon(M, N, K) → poly8, k_1, m, n
  15. OrthogonalLine(M, j) → f
  16. Line(N, xAxis) → p
  17. Intersect(p, f) → O
  18. Polygon(O, M, N) → poly9, n_1, o, m_1
  19. Intersect(l, f) → P
  20. Intersect(p, g_3) → Q
  21. Polygon(Q, P, O) → poly10, o_1, q, p_1
  22. Polygon(G, Q, P) → poly11, p_2, g_4, q_1
  23. Polygon(P, O, N, L) → poly12, p_3, o_2, n_2, l_1
  24. Polygon(Q, O, M, J) → poly13, q_2, o_3, m_2, j_1
  25. Rotate(I, 180*°, (5, -3)) → I'_1
  26. Rotate(E, 180*°, (5, -3)) → E'_2
  27. Rotate(H, 180*°, (5, -3)) → H'_1
  28. Midpoint(q) → R
  29. Midpoint(p_1) → S
  30. Midpoint(a_1) → T

AI Drawing Prompt Reference

Draw a right triangle to demonstrate the Pythagorean Theorem. Start by plotting the intersection of coordinate axes, then construct a quadrilateral and identify its centroid, vertex midpoints, and edge midpoints. Use these points to create multiple quadrilaterals and triangles, rotate and connect them to form interconnected geometric shapes, ultimately showing the geometric proof of the Pythagorean Theorem.
The prompt above was compiled from the original drawing commands and is for reference only.