Angles on the Same Arc

Angles on the Same Arc
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2015-01-13 15:55
In collections Circle Theorems
This example demonstrates the property that angles subtended by the same arc in a circle are equal. It involves core math concepts like the Circle Theorem, angles, and circle properties. Constructed using GeoGebra commands: Circle, Point, CircleArc, Segment, Angle. Suitable for middle school and above students learning circle theorems, geometric constructions, and theorem verification.

GeoGebra Commands & Parameters

  1. Circle(A, 4) → c_1
  2. Point(c_1) → E
  3. Point(c_1) → B
  4. CircleArc(A, E, B) → g
  5. Point(g) → D
  6. Point(g) → C
  7. Segment(B, C) → a
  8. Segment(E, C) → b
  9. Segment(B, D) → c
  10. Segment(E, D) → d
  11. CircleArc(A, B, E) → a_1
  12. Angle(B, C, E) → α
  13. Angle(B, D, E) → β
  14. Segment(B, A) → e
  15. Segment(E, A) → f
  16. Angle(B, A, E) → γ