MathPlotAI Logo MathPlotAI

Triangle Folding and Rotation Exploration

Triangle Folding and Rotation Exploration
Loading the math board and drawing, please wait…
2018-02-26 15:54
TrianglePolygonAngleTransformationGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates how a triangle and its associated figures are transformed through rotation and folding operations, allowing observation of changes in geometric properties. Core mathematical concepts include rotational symmetry of triangles, folding (reflection) transformations, construction of polygons and circular arcs, as well as tangent lines and intersection points. Construction highlights: using GeoGebra commands such as Polygon to create the initial triangle, Rotate to rotate the triangle and key points, Segment to connect lines, CircleArc to draw arcs, Line to construct lines, and Intersect to find intersection points; objects include multiple triangles (driehoek1 and its rotated copies), quadrilaterals (vierhoek), points (A, B, D, C, E, B', E', D', etc.), and auxiliary lines (a, b, c, d, e, f, g, h, k). Suitable for middle and high school geometry classes to study transformations, symmetry, and dynamic exploration, and for teachers to demonstrate the visual effects of folding and rotation.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Polygon(B, A, C, E) → vierhoek2, b_1, a_1, c_1, e
  3. Polygon(B, E, D) → driehoek1, d_1, b_2, e_1
  4. Rotate(B, (((s - 1) * 180))°, d_1) → B'
  5. Rotate(E, (((s - 1) * 180))°, d_1) → E'
  6. Rotate(D, (((s - 1) * 180))°, d_1) → D'
  7. Polygon(B', E', D') → driehoek1', d', b', e'
  8. Rotate(B, 180°, d_1) → B'_1
  9. Rotate(E, 180°, d_1) → E'_1
  10. Rotate(D, 180°, d_1) → D'_1
  11. Polygon(B'_1, E'_1, D'_1) → driehoek1'_1, d'_1, b'_1, e'_1
  12. Segment(B, E) → f
  13. Rotate(D, -90°, B) → DD
  14. CircleArc(B, DD, D) → g
  15. Segment(A, E) → h
  16. Rotate(C, -135°, E) → C'
  17. CircleArc(E, C', C, xOyPlane) → k
  18. Polygon(A, C, E) → driehoek2, e_2, a_2, c_2
  19. Rotate(A, (((s - 3) * 180))°, h) → A'
  20. Rotate(C, (((s - 3) * (-180)))°, h) → C'_1
  21. Rotate(E, (((s - 3) * (-180)))°, h) → E'_2
  22. Polygon(A', C'_1, E'_2) → driehoek2', e'_2, a', c'_1
  23. Polygon(D'_1, A, E) → driehoek3, e_3, d'_2, a_3
  24. Polygon(A, C, E, DD) → vierhoek3, i, j, l, m
  25. Line(D'_1, E) → n
  26. Intersect(n, e'_2) → F
  27. Segment(D'_1, F) → p
  28. Segment(F, E) → q