MathPlotAI Logo MathPlotAI

Pythagorean Theorem (Right Triangle_2)

Pythagorean Theorem (Right Triangle_2)
Loading the math board and drawing, please wait…
2020-05-15 03:23
TriangleAngleTrigonometryCoordinate Geometry
In collections Pythagorean Theorem
This example demonstrates the Pythagorean Theorem using a right triangle. It constructs the relationship between the sides of a right triangle to illustrate the core concept of the theorem. Commands used include Circle, Intersect, Segment, Rotate, Angle, Ray, Polygon, Textfield, SelectedElement, SelectedIndex, Point, If. Suitable for middle school and above students to learn geometric construction and the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Circle(B, 5) → c
  2. Circle(A, 12) → c_1
  3. Intersect(c, c_1) → D, E, ,
  4. Segment(A, B) → f
  5. Segment(A, C) → g
  6. Rotate(A, (-β), B) → Α'
  7. Angle(Α', B, A) → β_1
  8. Segment(A, B) → q
  9. Segment(B, C) → r
  10. Angle(C, B, A) → γ
  11. Ray(B, Α') → s
  12. Intersect(c, s) → G,
  13. Polygon(G, B, 4) → πολύγ3, t, a_1, b, d, G_1, H
  14. Segment(B, C) → e
  15. Angle(B, A, C) → δ
  16. Angle(A, C, B) → ε
  17. Textfield(empty1) → ΕισΑΒ2
  18. Textfield(empty2) → ΕισAC2
  19. Textfield(empty3) → ΕισBC2
  20. Textfield(empty4) → ΕισBC
  21. Textfield(empty5) → ΕισAC2kaiBC2
  22. Polygon(B, A, 4) → πολύγ1, h, j, k, h_1, Α, Β
  23. SelectedElement(L) → text5
  24. SelectedIndex(L) → v
  25. SelectedIndex(L1) → w
  26. Point(c_1) → I
  27. Rotate(B, ζ, A) → B'
  28. Angle(B, A, B') → η
  29. Segment(A, B') → m
  30. Intersect(c_1, m) → J,
  31. Polygon(A, J, 4) → poly1, n, p, b_1, d_1, K, M
  32. Textfield(empty7) → ΕισαΑC
  33. Textfield(empty6) → ΕισΑΒ
  34. If(ans5 ≟ 100, true, false) → AC2kaiBC2
  35. If(ans6 ≟ 13, true, false) → AB1
  36. If(ans1 ≟ 169, true, false) → AB2
  37. If(ans7 ≟ 12, true, false) → AC1
  38. If(ans2 ≟ 144, true, false) → AC2
  39. If(ans4 ≟ 5, true, false) → BC1
  40. If(ans3 ≟ 25, true, false) → BC2

AI Drawing Prompt Reference

Draw a right triangle ABC with A as the right angle. First, draw circles centered at A with radii 5 and 12, and their intersection points are B and C. Then draw line segments AB, AC, and BC, and angles BAC, ABC, and ACB. Next, use rotation and angles to construct auxiliary lines and segments, and finally label the lengths of each side and verify the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.