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Exploring Proportions in Right Triangles

Exploring Proportions in Right Triangles
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2016-01-01 02:36
TriangleCircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the proportional relationships in right triangles, focusing on geometric properties related to the incircle. It involves core math concepts like right triangle properties, incircle, Pythagorean theorem, trigonometry, and linear regression. The construction uses commands such as Segment, OrthogonalLine, Point, Angle, Intersect, Circle, Polygon in GeoGebra to build the figure and calculate side lengths a, b, c, and angles α, β, γ. It is suitable for high school mathematics education to explore and verify geometric theorems, enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Segment(A_1, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(B, C) → c
  5. Segment(A_1, C) → d
  6. Angle(A_1, B, C) → α
  7. OrthogonalLine(B, d) → e
  8. Intersect(e, d) → D
  9. Segment(B, D) → f
  10. Angle(B, D, A_1) → β
  11. Circle(D', Segment[D, A_1]) → g
  12. Point(g) → A
  13. Segment(D', A) → h
  14. OrthogonalLine(D', h) → i
  15. Circle(D', Segment[D, B]) → k
  16. Intersect(k, i, 2) → B'
  17. Segment(D', B') → j
  18. Segment(A, B') → l
  19. Angle(A, D', B') → γ
  20. Polygon(A_1, D, B) → poly1, b_1, a_1, d_1
  21. Polygon(B, D, C) → poly2, c_1, b_2, d_2
  22. Polygon(A, D', B') → poly3, b', a_2, d'
  23. Circle(D'', Segment[D, B]) → p
  24. Point(p) → B''
  25. Segment(D'', B'') → m
  26. Circle(D'', Segment[D, C]) → q
  27. OrthogonalLine(D'', m) → n
  28. Intersect(q, n, 2) → C''
  29. Segment(B'', C'') → r
  30. Polygon(B'', D'', C'') → poly4, c'', b'', d''
  31. Angle(B'', D'', C'') → δ
  32. Angle(D, A_1, B) → ε
  33. Angle(B, C, D) → ζ
  34. Angle(B', A, D') → η
  35. Angle(D', B', A) → θ
  36. Angle(C'', B'', D'') → ι
  37. Angle(D'', C'', B'') → κ