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Exploration of the Inner Triangle

Exploration of the Inner Triangle
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2019-09-02 21:15
TriangleFunctionGeometric Construction
In collections Exploring Feyman's Triangle
This example demonstrates the exploration of the inner triangle. Key mathematical concepts include triangles, function graphs, and geometric construction. Using GeoGebra commands such as Segment, Dilate, and Intersect, the inner triangle can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(C, B) → g
  3. Segment(A, C) → h
  4. Dilate(C, 1 / 3, A) → C'
  5. Dilate(A, 1 / 3, B) → A'
  6. Dilate(B, 1 / 3, C) → B'
  7. Segment(B, C') → i
  8. Segment(A, B') → j
  9. Segment(A', C) → k
  10. Intersect(k, i) → E
  11. Intersect(j, i) → D
  12. Intersect(k, j) → F
  13. Polygon(B, A, C) → t1, c, b, a
  14. Polygon(E, D, F) → t2, f_1, d, e
  15. PointIn(t2) → Pointt2
  16. Polygon(B, A', E) → t3, e_1, b_1, a'
  17. Polygon(A, C', D) → t4, d_1, a_1, c'
  18. Polygon(C, B', F) → t5, f_2, c_1, b'
  19. Polygon(A, A', E, D) → q1, a_2, l, e_2, d_2
  20. Polygon(B, B', F, E) → q2, b_2, m, f_3, e_3
  21. Polygon(C, C', D, F) → q3, c_2, n, d_3, f_4

AI Drawing Prompt Reference

Draw triangle ABC, then shrink the opposite sides by 1/3 from points A, B, and C to get A', B', and C'. Connect B to C', A to B', and A' to C, and find their intersections E, D, and F to form the inner triangle DEF.
The prompt above was compiled from the original drawing commands and is for reference only.