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Special Right Triangles by Chi Tran

Special Right Triangles by Chi Tran
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2014-10-07 11:07
TriangleTrigonometryCoordinate GeometryGeometric Construction
This example allows students to explore the properties of special right triangles and derive the inverse sine, cosine, and tangent functions through constructing the sides and angles of right triangles. Commands used include Intersect, Segment, Angle, Polygon, Midpoint, and Rotate. Suitable for middle and high school students learning trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(A, B) → c_2
  3. Segment(A, C) → b_2
  4. Segment(B, C) → a_2
  5. Angle(C, A, B) → β
  6. Angle(B, C, A) → δ
  7. Polygon(G, H, I) → poly2, i_1, g_4, h_4
  8. Angle(I, H, G) → ε
  9. Polygon(D, E, F) → poly1, f_1, d_1, e_1
  10. Angle(F, D, E) → γ
  11. Polygon(J, K, 3) → poly3, j_1, k_2, l_2, L
  12. Midpoint(J, K) → M
  13. Polygon(K, M, L) → poly4, l_1, k_1, m_1
  14. Polygon(N, O, P) → poly5, p_1, n_1, o_1
  15. Angle(K, M, L) → ζ
  16. Angle(N, O, P) → η
  17. Angle(L, K, M) → θ
  18. Angle(D, E, F) → ι
  19. Polygon(G_1, H_1, I_1) → poly2_1, i_2, g_5, h_5
  20. Angle(I_1, H_1, G_1) → ε_1
  21. Rotate(G_1, 90*°, Q) → R
  22. Rotate(H_1, 90*°, Q) → S
  23. Rotate(I_1, 90*°, Q) → T
  24. Polygon(R, S, T) → poly6, t_1, r_1, s_1
  25. Angle(T, S, R) → κ
  26. Segment(U, V) → a_1
  27. Rotate(D, 180*°, W) → D'
  28. Rotate(E, 180*°, W) → E'
  29. Rotate(F, 180*°, W) → F'
  30. Polygon(D', E', F') → poly1', f', d', e'
  31. Angle(F', D', E') → λ
  32. Angle(E', F', D') → μ
  33. Angle(D', E', F') → ν
  34. Angle(R, T, S) → ξ
  35. Angle(S, R, T) → ο

AI Drawing Prompt Reference

Draw a right triangle ABC with A on the x-axis and B on the y-axis, where C is the right angle. Construct sides AB, AC, and BC, and measure angles B and C. Then construct an isosceles right triangle DEF with C as the right angle, rotate it 90 degrees to get RST, and construct another congruent triangle D'E'F' and rotate it 180 degrees.
The prompt above was compiled from the original drawing commands and is for reference only.