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Constructing Triangle by 3 Sides

Constructing Triangle by 3 Sides
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2014-01-21 21:59
TriangleVectorCoordinate GeometryGeometric Construction
In collections Special Lines and Centres of Triangle
This example demonstrates how to construct a triangle precisely using three side lengths. It involves core mathematical concepts such as coordinate geometry, vector operations, and geometric construction. Key construction steps utilize GeoGebra commands and objects like Point, Segment, If, UnitOrthogonalVector, UnitVector, Polygon, and Intersect to calculate unit orthogonal and unit vectors for determining vertex positions. Suitable for high school mathematics instruction on triangle construction methods in analytical geometry.

GeoGebra Commands & Parameters

  1. Point(Sequence[C_0 + (1 + 0.1 * i, 0), i, 0, 140]) → C'_0
  2. Segment(C_0, C'_0) → a
  3. Point(Sequence[D_0 + (1 + 0.1 * i, 0), i, 0, 140]) → D'_0
  4. Segment(D_0, D'_0) → b
  5. Point(Sequence[E_0 + (1 + 0.1 * i, 0), i, 0, 140]) → E'_0
  6. Segment(E_0, E'_0) → c
  7. If(Max[{a, b, c}] ≟ b, -1, 1) → sign2
  8. Point(CircleArc[C, C + (a, 0), Rotate[C + (a, 0), 358*°, C]]) → C'
  9. If(Max[{a, b, c}] ≟ c, -1, 1) → sign1
  10. Point(Circle[A, 1]) → B
  11. Point(Circle[A', 1]) → B'
  12. UnitOrthogonalVector(Segment[A, B]) → v
  13. UnitVector(Segment[A, B]) → u
  14. Polygon(A, A - 0.5 * u, A - 0.5 * u - 1.5 * v, A - 1.5 * v + 15.5 * u, A + 15.5 * u, B) → poly1, a_1, b_1, c_1, d, e, f
  15. Segment(C, C') → g
  16. Polygon(C, C - 0.01 * UnitOrthogonalVector[g], C - 0.01 * UnitOrthogonalVector[g] + a * UnitVector[g], C + 0.01 * UnitOrthogonalVector[g] + a * UnitVector[g], C + 0.01 * UnitOrthogonalVector[g]) → poly2, h, i, j, k, l
  17. Point(CircleArc[D, D + (b, 0), Rotate[D + (b, 0), 358*°, D]]) → D'
  18. Segment(D, D') → m
  19. Polygon(D, D - 0.01 * UnitOrthogonalVector[m], D - 0.01 * UnitOrthogonalVector[m] + b * UnitVector[m], D + 0.01 * UnitOrthogonalVector[m] + b * UnitVector[m], D + 0.01 * UnitOrthogonalVector[m]) → poly3, n, p, q, r, s
  20. Point(CircleArc[E, E + (-c, 0), Rotate[E + (-c, 0), 358*°, E]]) → E'
  21. Segment(E, E') → t
  22. Polygon(E, E - 0.01 * UnitOrthogonalVector[t], E - 0.01 * UnitOrthogonalVector[t] + c * UnitVector[t], E + 0.01 * UnitOrthogonalVector[t] + c * UnitVector[t], E + 0.01 * UnitOrthogonalVector[t]) → poly4, d_1, e_1, f_1, g_1, h_1
  23. If(Distance[C, D] < 0.1, true, false) → connected1
  24. If(Distance[C', E] < 0.1, true, false) → connected2
  25. Point(CircleArc[C, C + (b, 0), Rotate[C + (b, 0), 358*°, C]]) → F
  26. Segment(C, F) → b'
  27. Point(CircleArc[C', C' - (c, 0), Rotate[C' - (c, 0), 358*°, C']]) → G
  28. Segment(C', G) → c'
  29. Intersect(Circle[C, b], Circle[C', c]) → H, I, ,
  30. Segment(C, H) → i_1
  31. Segment(C, I) → j_1
  32. Segment(C', H) → k_1
  33. Segment(C', I) → l_1
  34. Segment(C, H_1) → m_1
  35. Segment(C', H_2) → n_1

AI Drawing Prompt Reference

Draw a triangle by constructing three sides precisely. Start by drawing three perpendicular line segments as initial positions of the sides, then use arcs and vector calculations to determine the positions of the three vertices, and finally connect the vertices to form the triangle, labeling the three sides.
The prompt above was compiled from the original drawing commands and is for reference only.