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Area Ratio of Similar Triangles by Mathguru

Area Ratio of Similar Triangles by Mathguru
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2012-05-30 13:50
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the areas of similar triangles and the squares of their corresponding sides. By constructing similar triangles and measuring their sides and areas, students can intuitively understand the properties of similar triangles. The example uses commands such as Segment, Rotate, Angle, Ray, Intersect, Distance, and Polygon in GeoGebra. Suitable for middle school and above students to learn about geometry and triangle-related concepts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(A_1, B_1) → b
  3. Rotate(A, -α, B) → A'
  4. Angle(A', B, A) → β_1
  5. Rotate(B, β, A) → B'
  6. Angle(B, A, B') → γ
  7. Ray(A, B') → c
  8. Ray(B, A') → d
  9. Intersect(c, d) → C
  10. Segment(C, A) → e
  11. Segment(C, B) → f
  12. Rotate(B_1, β, A_1) → D
  13. Angle(B_1, A_1, D) → δ
  14. Rotate(A_1, -α, B_1) → E
  15. Angle(E, B_1, A_1) → ε
  16. Ray(A_1, D) → g
  17. Ray(B_1, E) → h
  18. Intersect(g, h) → C_1
  19. Segment(A_1, C_1) → i
  20. Segment(C_1, B_1) → j
  21. Distance(A, B) → distanceAB
  22. Distance(B, C) → distanceBC
  23. Distance(C, A) → distanceCA
  24. Distance(A_1, B_1) → distanceA1B1
  25. Distance(B_1, C_1) → distanceB1F
  26. Distance(C_1, A_1) → distanceFA1
  27. Polygon(B, C, A) → poly1, a_1, b_1, c_1
  28. Polygon(C_1, A_1, B_1) → poly2, b_2, c_2, a_2
  29. Angle(A_1, C_1, B_1) → ζ
  30. Angle(A, C, B) → η