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§10.1 GG Intersections Lesson

§10.1 GG Intersections Lesson
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2019-03-21 10:46
TriangleTrigonometryCoordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates dynamic relationships and geometric properties of intersections (like orthocenter, medians, vertices) in triangles; involves core concepts: intersection, orthocenter, cosine rule, median line, symmetry, subtraction; constructed using GeoGebra commands like Curve[Cartesian] with objects a, b, k, A, B, C, D, E, F, text, lines; suitable for high school mathematics teaching, integrating triangle geometry with coordinate geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian((sin((2 * t)), ℯ^(t), cos((2 * t))), t, 0, (2 * 3.141592653589793)) → a
  2. CurveCartesian(sin((2 * t)), ℯ^(t), cos((2 * t)), t, -10, 10) → b
  3. CurveCartesian((t^(2), cos((4 * t)), sin((3 * t))), t, -10, 10) → r
  4. CurveCartesian(t^(2), cos((4 * t)), sin((3 * t)), t, -10, 10) → c
  5. CurveCartesian((2 * cos(t)), (2 * sin(t)), ((2 * cos(t)))^(2), t, 0, 10) → f
  6. CurveCartesian(sin(t), cos(t), t, t, (-2 * π), (2 * π)) → h
  7. CurveCartesian((2 * t) + 1, (-t) + 2, t + 3, t, -5, 5) → i
  8. CurveCartesian((-3 * s) + 8, s - 1, (-2 * s) + 7, s, -10, 10) → j

AI Drawing Prompt Reference

Draw a dynamic triangle showing its vertices, medians, and orthocenter, with intersection points and relationships controlled by a slider, while adding several curves and lines to illustrate geometric properties and symmetry, starting from basic shapes and progressively incorporating medians, orthocenter, and other elements, finally outlining the overall structure with curves and lines.
The prompt above was compiled from the original drawing commands and is for reference only.