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Bisecting a Triangle

Bisecting a Triangle
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2015-11-08 11:37
TriangleAngleGeometric Construction
This example demonstrates how to bisect an angle of a triangle through a point on one side. It involves core mathematical concepts such as angle bisector, midpoint of a segment, and symmetry. Construction highlights include using GeoGebra commands/objects like Segment, Midpoint, Point, Line, Ray, Semicircle, Intersect, and Polygon; objects include A, B, a, C, b, c, M, P, d, e, f, g, h, F, poly1, f_1, a_1, e_1, poly2, c_1, a_2, b_1, D, E, i, drag, poly3, g_1, a_3, p. Suitable for middle school and above learning geometric constructions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Midpoint(B, C) → M
  5. Point(b) → P
  6. Segment(A, M) → d
  7. Segment(A, P) → e
  8. Line(M, e) → f
  9. Ray(M, P) → g
  10. Semicircle(B, C) → h
  11. Intersect(h, g) → F,
  12. Polygon(A, P, F) → poly1, f_1, a_1, e_1
  13. Polygon(A, B, C) → poly2, c_1, a_2, b_1
  14. Intersect(f, poly2) → D, E
  15. Segment(M, D) → i
  16. Point(i) → drag
  17. Polygon(A, P, drag) → poly3, g_1, a_3, p