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Exploring Special Right Triangles by tmoorehead

Exploring Special Right Triangles by tmoorehead
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2016-02-11 07:05
TriangleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to construct and explore the properties of 30°-60°-90° and 45°-45°-90° special right triangles using GeoGebra. It involves core mathematical concepts such as the side length ratios of triangles, angle relationships, the Pythagorean theorem, quadratic equations, ellipses, linear functions, and centroids. The construction utilizes commands like Point, Segment, Rotate, Angle, Line, and Intersect. It is suitable for high school mathematics students and teachers for learning and instructional demonstration.

GeoGebra Commands & Parameters

  1. Point(Circle[A, s]) → B
  2. Segment(A, B) → a
  3. Rotate(A, 270°, B) → C
  4. Rotate(B, 270°, B) → B'
  5. Segment(C, B') → a'
  6. Segment(A, C) → b
  7. Angle(C, B, A) → α
  8. Angle(B, A, C) → β
  9. Angle(A, C, B) → γ
  10. Point(Circle[X, s]) → Y
  11. Segment(X, Y) → d
  12. Rotate(Y, 60°, X) → Y'
  13. Angle(Y, X, Y') → δ
  14. Line(X, Y') → e
  15. Rotate(X, 270°, Y) → X'
  16. Angle(X', Y, X) → ε
  17. Line(Y, X') → f
  18. Intersect(e, f) → Z
  19. Segment(Y, Z) → g
  20. Segment(X, Z) → h
  21. Angle(X, Z, Y) → ζ