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Pythagorean Theorem (Acute Triangles)

Pythagorean Theorem (Acute Triangles)
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2020-05-15 03:24
TriangleCircleGeometric Construction
In collections Pythagorean Theorem
This example demonstrates the application of the Pythagorean Theorem in acute triangles. Key math concepts include the Pythagorean Theorem and properties of acute triangles. Construction highlights involve GeoGebra commands such as Circle, Intersect, Segment, Rotate, Angle, Ray, Polygon, Textfield, SelectedElement, Point, If, and Line. Suitable for middle school and above students to learn and understand the application of the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Circle(B, 6) → c
  2. Circle(A, 9) → 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) → inputBox1
  18. Textfield(empty2) → Εισ1
  19. Textfield(empty3) → Εισ2
  20. Textfield(empty4) → Εισ3
  21. Textfield(empty5) → Εισ4
  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(ans1 ≟ 100, true, false) → AB2
  35. If(ans2 ≟ 81, true, false) → AC2_1
  36. If(ans3 ≟ 36, true, false) → BC2
  37. If(ans6 ≟ 10, true, false) → AB1
  38. If(ans7 ≟ 9, true, false) → AC1
  39. If(ans4 ≟ 6, true, false) → BC1
  40. If(ans5 ≟ 117, true, false) → AC2

AI Drawing Prompt Reference

Draw an acute triangle ABC with points A, B, and C as its vertices. First, draw a circle c with center A and radius 6, and a circle c_1 with center B and radius 9, which intersect at points D and E. Then, draw line segments AB and AC, and use rotation and angles to construct line segments BD, BE, and BC. Construct a ray s starting from B that intersects circle c at point G. Through these steps, construct an acute triangle and use text fields to input side lengths and verify the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.