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Open Middle: Ambiguous Case Setups

Open Middle: Ambiguous Case Setups
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2022-01-24 10:34
CircleAngleTrigonometryGeometric Construction
This example demonstrates how to create an ambiguous case (SSA) setup in GeoGebra by dynamically adjusting side lengths and angles to show different solution scenarios. Core mathematical concepts involved include trigonometric functions (sine, cosine), geometric constructions, and the ambiguous triangle theorem. Construction highlights the use of GeoGebra commands like If, Ray, Intersect, Textfield, Mode, Polygon, Segment, Angle, Point, Circle, along with objects such as h, b, c, j, d, e_2, i, a, A, B, o, p, B', g, F, d_1, etc. Suitable for high school mathematics education to help students understand the diversity of solutions in ambiguous triangles.

GeoGebra Commands & Parameters

  1. If(o ≟ true, Circle[A, b], Circle[A, j]) → p
  2. If(o ≟ true, Rotate[B, (((10 * a) + i) * π / 180), A], Rotate[B, (((10 * d) + e_2) * π / 180), A]) → B'
  3. Ray(A, B') → g
  4. Intersect(p, g, 1) → F
  5. If(o ≟ true, Circle[F, c], Circle[F, h]) → d_1
  6. Textfield(a) → InputBox1
  7. Textfield(b) → InputBox2
  8. Textfield(c) → InputBox3
  9. Textfield(d) → InputBox4
  10. Textfield(e_2) → InputBox5
  11. Mode(l1) → l2
  12. Textfield(i) → InputBox6
  13. Textfield(j) → InputBox7
  14. If(Length[l2] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text7
  15. Textfield(h) → InputBox8
  16. Polygon(C, D, 3) → poly1, r, s, t, E
  17. Polygon(C_{1}, D_{1}, 3) → poly1_{1}, r_{1}, s_{1}, t_{1}, E_{1}
  18. Segment(C, D) → f_1
  19. Segment(D, E) → g_1
  20. Segment(E, C) → h_1
  21. Segment(C_{1}, D_{1}) → i_1
  22. Segment(D_{1}, E_{1}) → j_1
  23. Segment(E_{1}, C_{1}) → k_1
  24. Ray(A, B) → f
  25. Angle(B, A, B') → α
  26. Segment(A, F) → m
  27. Point(d_1) → G
  28. Segment(F, G) → q
  29. Circle(F, c) → c_1
  30. Intersect(d_1, f, 2) → H
  31. Intersect(d_1, f, 1) → I
  32. Polygon(A, F, H) → t1, h_2, a_1, f_2
  33. Polygon(A, F, I) → t2, i_2, a_2, f_3

AI Drawing Prompt Reference

Draw a triangle with two possible solutions by adjusting side lengths and angles. Start by creating point A, then construct a triangle with given side lengths b and c, and angle a. Next, change the position of angle B by adjusting side lengths d and e_2, forming a triangle with two possible solutions. Finally, use circles and segments to illustrate the different solutions of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.