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Pythagorean Theorem - Hypotenuse Calculation

Pythagorean Theorem - Hypotenuse Calculation
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2014-11-15 22:18
TrigonometryGeometric ConstructionSlider Animation
In collections Pythagoras
This example demonstrates the calculation of the hypotenuse in a right triangle by dynamically changing the lengths of the two legs. It involves the core mathematical concept of the Pythagorean Theorem. The construction uses commands/objects like Circle, Point, Segment, OrthogonalLine, Intersect, and Angle from GeoGebra. It is suitable for middle school students and above to learn and understand the application of the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Circle(A, b) → c_2
  2. Circle(A, c) → d
  3. Point(c_2) → C
  4. Segment(C, A) → e
  5. OrthogonalLine(A, e) → f
  6. Intersect(d, f, 2) → B
  7. Segment(A, B) → g
  8. Angle(C, A, B) → α
  9. Intersect(c_2, e, 1) → D
  10. Segment(B, D) → h
  11. Segment(A, D) → i
  12. Segment(C, B) → j
  13. Circle(A_1, b) → c_1
  14. Circle(A_1, c) → d_1
  15. Point(c_1) → B_1
  16. Segment(B_1, A_1) → e_1
  17. OrthogonalLine(A_1, e_1) → f_1
  18. Intersect(d_1, f_1, 2) → C_1
  19. Segment(A_1, C_1) → g_1
  20. Angle(B_1, A_1, C_1) → α_1
  21. Intersect(c_1, e_1, 1) → D_1
  22. Segment(C_1, D_1) → h_1
  23. Segment(A_1, D_1) → i_1
  24. Segment(B_1, C_1) → j_1

AI Drawing Prompt Reference

Draw a right triangle with two sliders to dynamically change the lengths of the legs, showing how the hypotenuse length changes. Draw circles with the legs as radii, connect the intersection points to form a triangle, and highlight the hypotenuse. Then, draw another triangle using the right-angle vertex as the center and the hypotenuse as the radius, demonstrating the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.