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Pythagoras' Theorem - Calculating the Hypotenuse

Pythagoras' Theorem - Calculating the Hypotenuse
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2014-09-15 15:14
TriangleAngleGeometric Construction
This example demonstrates how to use Pythagoras' Theorem to calculate the length of the hypotenuse in a right-angled triangle. Key mathematical concepts include the properties of right-angled triangles and Pythagoras' Theorem. By dragging the red vertices, you can change the dimensions of the triangle and observe the changes in the hypotenuse length. The construction uses commands such as Line, Point, Segment, Angle, Polygon, PointIn, and Intersect in GeoGebra. Suitable for middle school and above students learning geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. Segment(C, A) → b
  4. Line(A, D) → c
  5. Point(c) → E
  6. Segment(E, A) → d
  7. Segment(C, E) → e
  8. Angle(E, A, C) → α
  9. Polygon(C, E, 4) → poly1, f, g, h, i, F, G
  10. Polygon(E, A, 4) → poly2, j, k, l, m, H, I
  11. Polygon(A, C, 4) → poly3, n, p, q, r, J, K
  12. Line(A_1, B_1) → a_1
  13. Point(a_1) → C_1
  14. Segment(C_1, A_1) → b_1
  15. Line(A_1, D_1) → c_1
  16. Point(c_1) → E_1
  17. Segment(E_1, A_1) → d_1
  18. Segment(C_1, E_1) → e_1
  19. Angle(E_1, A_1, C_1) → α_1
  20. PointIn(poly1) → Pointpoly1
  21. PointIn(poly2) → Pointpoly2
  22. PointIn(poly3) → Pointpoly3
  23. Segment(C, E) → f_1
  24. Intersect(b, d) → L
  25. Segment(L, C) → g_1
  26. Point(g_1) → M

AI Drawing Prompt Reference

Draw a right-angled triangle with labeled legs and hypotenuse. Allow vertices to be dragged to change the triangle's size, showing the hypotenuse length adjust. Cover the triangle's three regions with three quadrilaterals, labeling the three angles. Finally, draw a line segment from the intersection of the legs to the hypotenuse, forming an auxiliary line.
The prompt above was compiled from the original drawing commands and is for reference only.