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Alternate Interior Angles Exploration

Alternate Interior Angles Exploration
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2018-10-22 10:40
AngleTransformationGeometric Construction
This applet helps students discover the alternate interior angles theorem by rotating an angle 180 degrees. It demonstrates key concepts such as angles and geometric transformations. Using GeoGebra commands like Rotate, Angle, and Line, students can visually understand the properties of alternate interior angles. Suitable for middle school and above students learning geometric transformations and angle relationships.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, J, H) → k
  13. CircleSector(C, H, K) → p
  14. CircleSector(A, E, G) → q
  15. CircleSector(A, G, D) → r
  16. CircleSector(A, F, E) → t
  17. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  18. Vector(A, A') → u
  19. Translate(t, u) → t'
  20. CircleArc(A, E, G) → c_1
  21. CircleArc(A, G, D) → f_1
  22. CircleArc(C, J, H) → h_1
  23. Vector(A, C) → v
  24. Midpoint(C, A) → L
  25. Rotate(q, (((-i) * 180))°, L) → q'
  26. Rotate(A, (((-i) * 180))°, L) → A'_1
  27. Segment(L, A'_1) → g
  28. Segment(C, L) → n
  29. Segment(L, A) → s
  30. Point(b) → M
  31. Point(b) → N
  32. Ray(C, M) → a_1
  33. Ray(A, N) → b_1
  34. Rotate(E, (((-i) * 180))°, L) → E'
  35. Ray(A'_1, E') → d_1
  36. Circle(A'_1, Distance[L, A'_1]) → e_1
  37. Intersect(e_1, d_1, 1) → O
  38. Segment(A'_1, O) → g_1
  39. Rotate(r, ((i * 180))°, L) → r'_2
  40. Rotate(A, ((i * 180))°, L) → A'_2
  41. Rotate(D, ((i * 180))°, L) → D'
  42. Segment(L, A'_2) → h
  43. Circle(A'_2, L) → k_1
  44. Ray(A'_2, D') → i_1
  45. Intersect(k_1, i_1) → P,
  46. Segment(A'_2, P) → j_1