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Similar Triangles by JUN CARL ALENTON

Similar Triangles by JUN CARL ALENTON
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2019-02-11 14:21
TriangleTrigonometryGeometric Construction
This example demonstrates the properties of similar triangles. By constructing similar triangles, you can observe that corresponding angles are equal and corresponding sides are proportional. Commands used include Polygon, AngularBisector, Intersect, Angle, Circle, Segment, Point, Rotate, OrthogonalLine, Midpoint, Line, and Textfield. Suitable for students at the junior high school level and above to learn about similar triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D) → poly1, c, a, b
  2. AngularBisector(c, b) → f, g
  3. AngularBisector(c, a) → d, e
  4. Intersect(e, g) → E
  5. Angle(A, B, D) → α
  6. Angle(B, A, D) → β
  7. Angle(B, D, A) → γ
  8. Circle(A', Segment[A', B']) → h
  9. Circle(D', Segment[D', B']) → k
  10. Intersect(h, k, 2) → F
  11. Polygon(B', A', F, D') → poly2, b', a', f_1, d'
  12. Segment(A', D') → i
  13. Circle(A', 3) → p
  14. Point(p) → G
  15. Segment(G, A') → j
  16. Angle(D', A', G) → Θ
  17. Rotate(B', Θ - 180°, A') → B''
  18. Rotate(A', Θ - 180°, A') → A''
  19. Rotate(F, Θ - 180°, A') → F'
  20. Rotate(D', Θ - 180°, A') → D''
  21. Polygon(B'', A'', F', D'') → poly2', b'', a'', f', d''
  22. Polygon(B'', A', D'') → poly3, d''_1, b''_1, a'_1
  23. Polygon(A', F', D'') → poly4, d''_2, a'_2, f'_1
  24. OrthogonalLine(A', b''_1) → l
  25. Point(l) → H
  26. Segment(H, A') → m
  27. Angle(D'', A', B'') → δ
  28. Angle(A', B'', D'') → ε
  29. Angle(B'', D'', A') → ζ
  30. Midpoint(d''_1) → I
  31. Midpoint(a'_1) → J
  32. Midpoint(b''_1) → K
  33. Midpoint(d''_2) → L
  34. Midpoint(a'_2) → M
  35. Angle(A', D'', F') → θ
  36. Line(A', xAxis) → b_1
  37. Intersect(p, b_1, 1) → O
  38. Angle(F', A', D'') → ι
  39. Angle(D'', F', A') → κ
  40. Textfield(scale) → inputBox1
  41. Textfield(scale) → inputBox1_1
  42. Textfield(scale) → inputBox1_2

AI Drawing Prompt Reference

Draw two similar triangles. Start by constructing triangle ABD with points A, B, and D. Then, construct the angle bisectors of angles BAC and BAD, intersecting at point E. Next, construct circles and point F, and then construct triangle B'AF'D'. Rotate points B', A', F', and D' to form triangle B''A''F''D''. Finally, construct line segments and a circle from point A', find point H, and construct triangle B''A'D'', locating its midpoints I, J, K, L, and M, ensuring corresponding angles are equal and corresponding sides are proportional.
The prompt above was compiled from the original drawing commands and is for reference only.