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Illustration of a Proof of Pythagoras' Theorem

Illustration of a Proof of Pythagoras' Theorem
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2015-06-06 14:02
TrianglePolygonGeometric Construction
This example demonstrates Pythagoras' Theorem through geometric figures. It involves the relationship between the sides of a right-angled triangle. By constructing multiple polygons and using the translate command, it intuitively proves that the square of the hypotenuse equals the sum of the squares of the other two sides. Suitable for students at junior high school level and above.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → C
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Translate(Polygon[Rotate[A, -1.5707963267948966, Vertex[poly1, 3]], Rotate[B, -1.5707963267948966, Vertex[poly1, 3]], Rotate[C, -1.5707963267948966, Vertex[poly1, 3]]], Segment[Vertex[poly1, 3], Vertex[poly1, 2]]) → poly2
  6. Translate(Rotate[poly2, -1.5707963267948966, Vertex[poly2, 3]], Segment[Vertex[poly2, 3], Vertex[poly2, 2]]) → poly3
  7. Translate(Rotate[poly3, -1.5707963267948966, Vertex[poly3, 3]], Segment[Vertex[poly3, 3], Vertex[poly3, 2]]) → poly4
  8. Name(c) → A1_1
  9. Name(a) → B1_1
  10. Name(b) → C1_1
  11. Name(c) → D1_1
  12. Name(a) → B1_2
  13. Name(c) → D1_2
  14. Name(a) → B1_3
  15. Name(c) → D1_3
  16. Name(a) → B1_4
  17. Name(b) → C1_2
  18. Name(a) → B1_5
  19. Name(c) → D1_4
  20. Name(b) → C1_3
  21. Name(c) → D1_5
  22. Name(a) → A1_2
  23. Name(b) → B1_6
  24. Name(c) → C1_4

AI Drawing Prompt Reference

Draw a right-angled triangle and demonstrate the Pythagorean theorem. Start by plotting the intersection of the x and y axes, and points on each axis to form the triangle. Then, rotate and translate this triangle to create multiple similar polygons, visually showing that the square of the hypotenuse equals the sum of the squares of the other two sides.
The prompt above was compiled from the original drawing commands and is for reference only.