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Incenter Exploration by Tim Brzezinski

Incenter Exploration by Tim Brzezinski
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2015-08-10 05:07
TriangleCircleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems Triangles: Points of Concurrency
This example uses additional scaffolding to help students explore the incenter and incircle of a triangle. Key concepts include: ① definition of the incenter; ② properties of the incircle; ③ construction using GeoGebra commands. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Slope(f) → m
  3. PointIn(b) → C
  4. Segment(B, C) → g
  5. Segment(C, A) → h
  6. Polygon(A, B, C) → poly1, c, a_1, b_1
  7. Angle(poly1) → α, β, γ
  8. Rotate(B, α / 2, A) → B'
  9. Angle(B, A, B') → δ
  10. Line(A, B') → i
  11. Intersect(g, i) → D
  12. Rotate(A, γ / 2, C) → A'
  13. Angle(A, C, A') → ε
  14. Line(C, A') → j
  15. Intersect(j, f) → E
  16. Rotate(C, β / 2, B) → C'
  17. Angle(C, B, C') → ζ
  18. Line(B, C') → k
  19. Intersect(k, h) → F
  20. Ray(C, E) → n
  21. Ray(B, F) → p
  22. Intersect(p, n) → I
  23. Angle(I, A, C) → η
  24. Angle(E, C, B) → θ
  25. Angle(F, B, A) → ι
  26. Ray(A, I) → l
  27. Line(A, C) → q
  28. Slope(q) → m_1
  29. OrthogonalLine(I, f) → r
  30. OrthogonalLine(I, g) → s
  31. OrthogonalLine(I, h) → t
  32. Intersect(t, h) → G
  33. Intersect(r, f) → H
  34. Intersect(s, g) → J
  35. Segment(I, H) → e
  36. Segment(I, J) → f_1
  37. Segment(I, G) → g_1
  38. Angle(I, H, A) → κ
  39. Angle(I, J, B) → λ
  40. Angle(I, G, C) → μ