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Exploring Same-Side Exterior Angles

Exploring Same-Side Exterior Angles
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2019-06-24 22:45
AngleTransformationGeometric Construction
This example demonstrates the properties of same-side exterior angles. By using rotation and angle measurement, students can intuitively understand the definition and application of same-side exterior angles in geometry. The construction process involves commands such as point, rotate, angle, line, circle, and intersect. Suitable for middle school and above students to learn 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, K, I) → g
  13. CircleSector(C, I, J) → h
  14. CircleSector(C, J, H) → k
  15. CircleSector(C, H, K) → p
  16. CircleSector(A, D, F) → s
  17. CircleSector(A, F, E) → t
  18. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  19. Vector(A, A') → u
  20. Translate(s, u) → s'
  21. Translate(t, u) → t'
  22. CircleArc(C, K, I) → d_1
  23. CircleArc(C, I, J) → e_1
  24. CircleArc(A, D, F) → g_1
  25. CircleArc(A, F, E) → k_1