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Exploring Reflections by Ashley Moss

Exploring Reflections by Ashley Moss
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2017-10-13 22:36
TriangleCircleVectorTransformationGeometric Construction
This example demonstrates the reflection of triangle vertices about a point and its properties, involving core math concepts like reflection, circumcircle, arithmetic mean, normal distribution, and conditional probability. It uses commands such as Mirror, Polygon, Angle, Vector, Translate, Segment, and Midpoint in GeoGebra for construction. Suitable for high school students and educators exploring the intersection of geometric transformations and probability statistics.

GeoGebra Commands & Parameters

  1. Mirror(C, h) → C'
  2. Mirror(B, h) → B'
  3. Mirror(A, h) → A'
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Angle(A, B, C) → ABC
  6. Angle(B, C, A) → BCA
  7. Angle(C, A, B) → CAB
  8. Vector(D, E) → u
  9. Translate(A, u) → A'_2
  10. Translate(B, u) → B'_2
  11. Translate(C, u) → C'_2
  12. Polygon(A'_2, B'_2, C'_2) → poly1', c'_2, a'_2, b'_2
  13. Angle(B', C', A') → A'C'B'
  14. Angle(C', A', B') → B'A'C'
  15. Angle(A', B', C') → A'B'C'
  16. Segment(D, F) → f
  17. Segment(E, F) → g
  18. Midpoint(f) → G
  19. Midpoint(g) → H
  20. Polygon(A', B', C') → poly1'_1, c', a', b'

AI Drawing Prompt Reference

Draw triangle ABC, then reflect it over point h to get A'B'C'. Construct the circumcircle of triangle ABC. Translate A', B', and C' along vector u to get A'_2, B'_2, and C'_2, and then draw the circumcircle of triangle A'_2B'_2C'_2. Finally, measure and display the angles of triangles ABC, A'B'C', and their translated triangle.
The prompt above was compiled from the original drawing commands and is for reference only.