Pythagoras, Semicircles and Lunes - Lesson+Exploration

Pythagoras, Semicircles and Lunes - Lesson+Exploration
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2019-09-30 18:39
This example demonstrates the area equivalence between semicircles, triangles, and lunes, illustrating the Pythagorean theorem. Key math concepts include circle area, triangle area, geometric constructions, and right triangles. It is constructed using GeoGebra commands like Segment, Semicircle, Point, Polygon, Midpoint, Angle, and Mirror. Suitable for middle school and high school students learning geometry proofs and area calculations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Semicircle(A, B) → c
  3. Point(c) → C
  4. Polygon(A, B, C) → poli1, c_1, a_1, b
  5. Semicircle(A, C) → d
  6. Semicircle(C, B) → e
  7. Semicircle(B, A) → f
  8. Midpoint(b) → D
  9. Midpoint(a_1) → E
  10. Midpoint(a) → F
  11. Angle(A, C, B) → α
  12. Mirror(f, a) → f'
  13. Point(d) → G
  14. Point(e) → H
  15. Point(f) → I