Similar Right Triangles by Susan Addington

Similar Right Triangles by Susan Addington
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2016-03-04 02:41
This example demonstrates the construction of three similar right triangles by drawing an altitude to the hypotenuse of one right triangle. It involves core mathematical concepts such as geometric construction, similar triangles, right triangles, and geometric transformations. The construction uses commands and objects like Point, LineBisector, Segment, Intersect, Semicircle, CircleArc, OrthogonalLine, Polygon, Rotate, Dilate, Angle, Mirror in GeoGebra. Suitable for high school mathematics education to understand the properties of similar triangles and the application of geometric transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. LineBisector(A, B) → g
  4. Segment(A, B) → a
  5. Intersect(g, a) → F
  6. Semicircle(A, B) → c
  7. Intersect(c, g, 1) → E
  8. CircleArc(F, B, E) → h
  9. Point(h) → C
  10. Segment(C, B) → b
  11. Segment(C, A) → d
  12. OrthogonalLine(C, a) → e
  13. Intersect(e, a) → D
  14. Segment(C, D) → f
  15. Polygon(C, D, B) → poly1, b_1, c', d_1
  16. Rotate(C, rotate_1, D) → C'
  17. Rotate(D, rotate_1, D) → D'
  18. Rotate(B, rotate_1, D) → B'
  19. Polygon(C', D', B') → poly1', b', c'_1, d'
  20. Dilate(C', scale_1, D) → C''
  21. Dilate(D', scale_1, D) → D''
  22. Dilate(B', scale_1, D) → B''
  23. Polygon(C'', D'', B'') → poly1'', b'', c'', d''
  24. Angle(A, C, B) → α
  25. Angle(B, A, C) → γ
  26. Polygon(A, D, C) → poly2, c_1, a_1, d_2
  27. Mirror(A, xAxis) → A'
  28. Mirror(D, xAxis) → D'_1
  29. Mirror(C, xAxis) → C'_1
  30. Polygon(A', D'_1, C'_1) → poly2', c'_2, a', d'_1
  31. Rotate(A', rotate, A) → A''
  32. Rotate(D'_1, rotate, A) → G
  33. Rotate(C'_1, rotate, A) → H
  34. Polygon(A'', G, H) → poly2'', h_1, a'', g_1
  35. Dilate(A'', scale, A) → A'''
  36. Dilate(G, scale, A) → G'
  37. Dilate(H, scale, A) → H'
  38. Polygon(A''', G', H') → poly2''', h', a''', g'
  39. Angle(A, C, D) → δ
  40. Angle(D, C, B) → ε
  41. Angle(C, B, D) → ζ
  42. Angle(C, D, A) → η
  43. Angle(B, D, C) → β

AI Drawing Prompt Reference

Draw a right triangle with a perpendicular from the midpoint of the hypotenuse intersecting it, connect the intersection point to the endpoints of the hypotenuse to form three similar right triangles, and show two of them obtained by rotation and dilation.
The prompt above was compiled from the original drawing commands and is for reference only.