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CP Geometry Similar Figures and Ratios: Dynamic Demonstration

CP Geometry Similar Figures and Ratios: Dynamic Demonstration
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2018-11-16 05:40
TriangleCoordinate GeometryTransformationGeometric Construction
①This GeoGebra example dynamically demonstrates two similar triangles and the proportional relationships between their corresponding sides, illustrating the properties of similar figures. ②Core mathematical concepts include similar triangles, proportionality of corresponding sides, scale factor, and the use of dilation to generate similar shapes. ③Construction highlights: The Polygon command creates the original triangle ABC; the Dilate command generates the similar triangle A'B'C' by scaling about a center; the Distance command measures corresponding side lengths (e.g., distanceCB, distanceC'B'), with Text commands displaying these measurements; Angle commands mark angles to verify equality of corresponding angles. ④Suitable for middle or high school geometry lessons on similar figures and ratios, serving as an interactive tool for classroom demonstration or student exploration.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Dilate(A, 2, D) → A'
  3. Dilate(B, 2, D) → B'
  4. Dilate(C, 2, D) → C'
  5. Polygon(A', B', C') → t1', c', a', b'
  6. Distance(C, B) → distanceCB
  7. Distance(C', B') → distanceC'B'
  8. Distance(B, A) → distanceBA
  9. Distance(A, C) → distanceAC
  10. Distance(C', A') → distanceC'A'
  11. Distance(A', B') → distanceA'B'
  12. Distance(B', A') → distanceB'A'
  13. Distance(A', C') → distanceA'C'
  14. Angle(A, B, C) → α
  15. Angle(C, A, B) → β
  16. Angle(B, C, A) → γ
  17. Angle(C', A', B') → δ
  18. Angle(A', B', C') → ε
  19. Angle(B', C', A') → ζ