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Thales' Theorem GeoGebra Exploration

Thales' Theorem GeoGebra Exploration
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2016-05-04 20:26
CircleAngleTrigonometryParametric EquationGeometric Construction
In collections Circles (Theorems) Inscribed Angle Theorem: Discovery and Proof
This example demonstrates Thales' Theorem using GeoGebra: an inscribed angle intercepting a semicircle is a right angle. It involves core concepts like circles, angles, right triangles, and parametric equations. Construction uses commands such as Circle, Point, Line, Intersect, CircleArc, Dilate, Segment, Angle. Suitable for high school geometry instruction and construction learning.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(C, A) → a
  4. Intersect(c, a, 2) → D
  5. CircleArc(A, C, D) → d
  6. CircleArc(A, D, C) → e
  7. Point(e) → E
  8. Dilate(E, 1 - b, C) → E'
  9. Dilate(E, 1 - b, D) → E'_1
  10. Segment(E, E') → f
  11. Angle(C, E, D) → α
  12. Segment(E, E'_1) → g
  13. Segment(C, D) → h