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Summary of Conditions for Similarity of Triangles

Summary of Conditions for Similarity of Triangles
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2018-11-27 22:30
TriangleAngleGeometric Construction
This example demonstrates the conditions for triangle similarity (AA, SAS, SSS) and their applications. Core math concepts include triangle similarity theorems, angle-side relationships. GeoGebra commands used: Polygon, Translate, If, Midpoint, InteriorAngles. Suitable for high school students learning triangle similarity criteria and applications.

GeoGebra Commands & Parameters

  1. SelectedElement(listK) → k
  2. Polygon(C, A, B) → t1, a, b, c
  3. Translate(D, Vector[(k * Vector[A, C])]) → F
  4. Translate(D, Vector[(k * Vector[A, B])]) → E
  5. If(lang ≟ 1, {"", "AAA", "三邊成比例", "兩邊成比例且夾角相等"}, {"", "AAA", "3 sides proportional", "2 sides proportional and included angle equal"}) → listCondition
  6. Polygon(D, E, F) → t2, b', d, a'
  7. Midpoint(c) → G
  8. Midpoint(b) → H
  9. Midpoint(a) → I
  10. Midpoint(d) → J
  11. Midpoint(b') → K
  12. Midpoint(a') → L
  13. InteriorAngles(t1) → α, β, γ
  14. InteriorAngles(t2) → δ, ε, ζ