MathPlotAI Logo MathPlotAI

Congruence Transformations of a Triangle

Congruence Transformations of a Triangle
Loading the math board and drawing, please wait…
2015-01-13 22:38
TriangleTransformationGeometric Construction
This example explores the congruence of a triangle through simple geometric transformations. Key concepts include congruence transformations, geometric transformations, and centroid or barycenter. It uses commands like Polygon, Line, Mirror, Vector, Translate, and Rotate in GeoGebra. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(E, F) → e
  3. Mirror(A, e) → A'_1
  4. Mirror(B, e) → B'_1
  5. Mirror(C, e) → C'_1
  6. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  7. Vector(G, H) → u
  8. Translate(A, u) → A'_2
  9. Translate(B, u) → B'_2
  10. Translate(C, u) → C'_2
  11. Polygon(A'_2, B'_2, C'_2) → poly1'_2, c'_2, a'_2, b'_2
  12. Rotate(A, β, D) → A'
  13. Rotate(B, β, D) → B'
  14. Rotate(C, β, D) → C'
  15. Polygon(A', B', C') → poly1', c', a', b'

AI Drawing Prompt Reference

Draw a triangle ABC, then perform a mirror transformation with line EF as the axis to get A'_1, B'_1, C'_1, forming triangle A'_1B'_1C'_1. Next, perform a translation transformation with vector GH as the direction to get A'_2, B'_2, C'_2, forming triangle A'_2B'_2C'_2. Finally, rotate points A, B, C around point D by angle β to get A', B', C', forming the final triangle A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.