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Triangle Family

Triangle Family
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2016-04-08 09:00
TriangleCalculusGeometric Construction
This example demonstrates a pattern of equal-area triangles. It involves core math concepts like area calculation, tangent function, calculus, median line, geometric distribution, and kite. Construction highlights include using Polygon, Sequence, Line, OrthogonalLine, and Intersect commands in GeoGebra. Suitable for high school and above learners exploring geometric constructions and calculus applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Sequence(B + ((i * delta) * (B - A)), i, 1, N) → list1
  3. Line(A, B) → d
  4. OrthogonalLine(C, d) → e
  5. Intersect(e, d) → D
  6. Sequence(A + ((D - A) * Distance[Element[list1, i], A] / Distance[A, B]) + ((u * 2) * poly1 / Distance[A, Element[list1, i]]), i, 1, N) → list2
  7. Sequence(Polygon[A, Element[list1, i], Element[list2, i]], i, 1, N) → list3

AI Drawing Prompt Reference

Draw a series of equal-area triangles. First, draw triangle ABC. Then, generate a series of points evenly distributed along line segment AB. From point C, draw a perpendicular line to AB and find the intersection point D. Using these points and point D, construct a series of new triangles, ensuring each new triangle has the same area as triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.