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Angle Values Calculation and Reflection Demo

Angle Values Calculation and Reflection Demo
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2015-12-10 09:17
AngleVectorTrigonometryCoordinate GeometryGeometric Construction
In collections iShortcut Geometry Vol. 1: Lines & Angles
This example demonstrates the calculation and properties of angle values through geometric transformations involving a semicircle, intersection points, and reflections. Key mathematical concepts include natural numbers, rational numbers, standard deviation, 2D vectors, reflection transformations, and angle measurement. The construction uses GeoGebra commands like Point, Semicircle, Intersect, Segment, Mirror, and Angle. Suitable for high school mathematics education to understand the connection between geometric transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c_1
  4. Intersect(xAxis, yAxis) → D
  5. Point(c_1) → C
  6. Segment(C, D) → a
  7. Mirror(C, D) → C'
  8. Mirror(D, D) → D'
  9. Segment(C', D') → a'
  10. Angle(B, D, C) → α
  11. Segment(A, B) → b
  12. Angle(A, D, C') → β
  13. Angle(C', D, B) → d
  14. Angle(C, D, A) → c