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Midpoints of Triangle and Reflected Segments

Midpoints of Triangle and Reflected Segments
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2017-08-03 09:08
TriangleGeometric Construction
This example demonstrates the geometric relationships between the midpoints of a triangle and reflected segments. Key concepts include midpoints, reflections, and segments. Using GeoGebra commands such as Polygon, AngularBisector, Mirror, Segment, and Midpoint, one can construct a triangle, its midpoints, and reflected segments. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. AngularBisector(a, b) → f, g
  3. Mirror(B, f) → B'
  4. AngularBisector(a, c) → h, i
  5. Mirror(C, h) → C'_1
  6. Mirror(A, h) → A'_1
  7. AngularBisector(b, c) → j, k
  8. Mirror(B, j) → B'_1
  9. Segment(A2, A2 + (t4 * (B3 - A2))) → q
  10. Mirror(C, j) → C'
  11. Mirror(A, f) → A'
  12. Segment(C3, C3 + (t4 * (A1 - C3))) → r
  13. Polygon(A1, B1, C) → poly2, c_1, a1, b1
  14. Midpoint(b) → E
  15. Midpoint(a) → F
  16. Midpoint(c) → G
  17. Polygon(A2, B, C2) → poly3, c2, a2, b_1
  18. Polygon(A, B3, C3) → poly4, c3, a_1, b3
  19. Midpoint(q) → D
  20. Segment(B1, B1 + (t4 * (C2 - B1))) → p
  21. Midpoint(p) → H
  22. Midpoint(r) → I
  23. Ray(I, E) → s
  24. Ray(D, G) → t
  25. Intersect(t, s) → J
  26. Segment(I, I + (t6 * (J - I))) → l
  27. Segment(D, D + (t6 * (J - D))) → n_1
  28. Segment(H, H + (t6 * (J - H))) → m