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Naming Congruent and Similar Triangles

Naming Congruent and Similar Triangles
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2016-07-07 09:00
TriangleAngleGeometric Construction
This example demonstrates how to dynamically visualize and name congruent and similar triangles using GeoGebra. It covers core concepts like SSS, SAS, ASA, AAS for congruence and AA, SAS, SSS for similarity. Key GeoGebra commands and objects used include Sequence, RandomElement, Rotate, Line, Intersect, Circle, If, Max, Polygon, Min, Shuffle, Angle, Take, Append to generate and transform triangles. Suitable for middle school and above mathematics education for geometric construction and theorem verification.

GeoGebra Commands & Parameters

  1. Sequence(30° + ((i * 10))°, i, 0, 12) → listAlpha
  2. RandomElement(listAlpha) → α
  3. Sequence(((i * 10))°, i, 1, (180 - α / °) / 10 - 1) → listBeta
  4. RandomElement(listBeta) → β
  5. RandomElement({0.75, 1, 1.25}) → k
  6. Rotate(A, β, O) → A'
  7. Line(O, A') → LineOA'
  8. Rotate(O, (-α), A) → O'
  9. Line(A, O') → LineAO'
  10. Intersect(LineOA', LineAO') → B
  11. Circle(O'', (Distance[O, B] * k)) → c
  12. Rotate(Dilate[Translate[A, Vector[O, O'']], k, O''], If[rotate, theta, 0°], O'') → A''
  13. Circle(A'', (Distance[A, B] * k)) → d
  14. Intersect(c, d, 1) → B''1
  15. Intersect(c, d, 2) → B''2
  16. If(reflect, B''1, B''2) → B''
  17. Max({Distance[A, B], Distance[A, O], Distance[O, B]}) → maxLength
  18. Max({x(O), x(A), x(B), x(O''), x(A''), x(B'')}) → maxX
  19. Polygon(O, A, B) → poly1, b_1, c_1, a_1
  20. Min({x(O), x(A), x(B), x(O''), x(A''), x(B'')}) → minX
  21. Min({y(O), y(A), y(B), y(O''), y(A''), y(B'')}) → minY
  22. Max({y(O), y(A), y(B), y(O''), y(A''), y(B'')}) → maxY
  23. Shuffle({"D", "E", "F", "G", "H", "J", "K", "L", "M", "N", "P", "Q", "R", "S", "T", "V", "W", "X", "Y"}) → listLetter
  24. Angle(poly1) → angleO, angleA, angleB
  25. Polygon(B'', O'', A'') → poly2, a_2, b_2, c_2
  26. Angle(poly2) → angleB'', angleO'', angleA''
  27. Take(listLetter, 1, 3) → listQuestion
  28. Append("?", Take[listLetter, 4, 6]) → listAnswer1
  29. Append("?", Take[listLetter, 4, 6]) → listAnswer2
  30. Append("?", Take[listLetter, 4, 6]) → listAnswer3
  31. If(SelectedIndex[listAnswer1] ≟ 2, angleO'', If[SelectedIndex[listAnswer1] ≟ 3, angleA'', If[SelectedIndex[listAnswer1] ≟ 4, angleB'', 0°]]) → ans1
  32. If(SelectedIndex[listAnswer2] ≟ 2, angleO'', If[SelectedIndex[listAnswer2] ≟ 3, angleA'', If[SelectedIndex[listAnswer2] ≟ 4, angleB'', 0°]]) → ans2
  33. If(SelectedIndex[listAnswer3] ≟ 2, angleO'', If[SelectedIndex[listAnswer3] ≟ 3, angleA'', If[SelectedIndex[listAnswer3] ≟ 4, angleB'', 0°]]) → ans3