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Pythagorean Theorem by kneido

Pythagorean Theorem by kneido
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2014-05-16 17:59
TriangleCircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Key mathematical concepts include right triangles, Pythagorean Theorem, and geometric construction. It uses commands such as Semicircle, Point, Polygon, Angle, OrthogonalLine, Circle, Intersect, Line, Midpoint in GeoGebra. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Semicircle(A, B) → c_2
  2. Point(c_2) → C
  3. Polygon(A, B, C) → poly1, c, a, b
  4. Angle(poly1) → α, β, γ
  5. OrthogonalLine(C, a) → d
  6. OrthogonalLine(B, a) → e
  7. Circle(C, B) → f
  8. Intersect(f, d, 1) → D
  9. Line(D, a) → g
  10. Intersect(e, g) → E
  11. Polygon(C, B, E, D) → poly2, c_1, b_1, e_1, d_1
  12. OrthogonalLine(C, b) → h
  13. OrthogonalLine(A, b) → i
  14. Circle(A, C) → k
  15. Intersect(k, i) → F, G
  16. Line(F, b) → j
  17. Intersect(h, j) → H
  18. Polygon(A, C, H, F) → poly3, a_1, c_3, h_1, f_1
  19. OrthogonalLine(A, c) → l
  20. OrthogonalLine(B, c) → m
  21. Circle(B, A) → p
  22. Intersect(p, m, 1) → I
  23. Line(I, c) → n
  24. Intersect(l, n) → J
  25. Polygon(A, B, I, J) → poly4, a_3, b_2, i_1, j_1
  26. Midpoint(A, I) → K
  27. Midpoint(C, E) → L
  28. Midpoint(A, H) → M

AI Drawing Prompt Reference

Draw a right triangle with its three sides and three angles labeled. Create two semicircles with the legs as diameters, connecting their intersection points to the right angle vertex to form two smaller triangles. Draw circles with the hypotenuse and each leg as diameters, marking their intersections. Connect these points to form four new quadrilaterals. Label the midpoints of these quadrilaterals and connect them.
The prompt above was compiled from the original drawing commands and is for reference only.