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From Triangle to Parallelogram (I)

From Triangle to Parallelogram (I)
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2016-07-08 00:44
OptimizationGeometric Construction
This example demonstrates how to construct a parallelogram from a triangle and explore its geometric properties. Core math concepts include parallelogram, special points, optimization problems, set theory, exponential functions, and cones. Construction highlights involve commands/objects like Polygon, Line, Midpoint, Circle, Intersect, and OrthogonalLine from GeoGebra. Suitable for high school mathematics teaching, focusing on geometric construction and property investigation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(D, E) → f
  3. Line(D, F) → g
  4. Midpoint(B, C) → G
  5. Circle(D, Segment[G, C]) → d
  6. Intersect(d, f, 2) → H
  7. Line(H, g) → h
  8. OrthogonalLine(A, a) → i
  9. Intersect(i, a) → I
  10. Circle(H, Segment[A, I]) → e
  11. OrthogonalLine(H, f) → j
  12. Intersect(e, j, 2) → J
  13. Line(J, f) → k
  14. Intersect(k, h) → K
  15. Intersect(k, g) → L
  16. Polygon(L, K, H, D) → target, l, k_1, h_1, d_1

AI Drawing Prompt Reference

Draw a triangle ABC first, then construct a parallelogram ABCD. Start by connecting points A, B, and C to form the triangle. Next, use point D to draw a line parallel to BC and another parallel to AC to find the other two vertices H and L of the parallelogram. Finally, connect these points to form the parallelogram.
The prompt above was compiled from the original drawing commands and is for reference only.