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Vertically Opposite Angles

Vertically Opposite Angles
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2015-02-15 11:41
AngleTransformationGeometric Construction
In collections Angles 1
This example demonstrates the geometric properties and angle measure relationships of vertically opposite angles. It involves core math concepts like angles, geometric transformations, and angle measurement. Construction highlights the use of GeoGebra commands and objects such as Point, Segment, Rotate, and Angle. Suitable for middle school mathematics instruction to visually understand the equality of vertically opposite angles.

GeoGebra Commands & Parameters

  1. Point(Circle[C, 5]) → A
  2. Segment(C, A) → a
  3. Point(Circle[C, 5]) → B
  4. Segment(C, B) → b
  5. Rotate(A, 180*°, C) → A'
  6. Angle(A, C, A') → α
  7. Segment(C, A') → c
  8. Rotate(B, 180*°, C) → B'
  9. Angle(B, C, B') → β
  10. Segment(B', C) → d
  11. Angle(B', C, A) → η
  12. Angle(B, C, A') → θ

AI Drawing Prompt Reference

Draw a circle with center C and radius 5, and take points A and B on the circle. Connect CA and CB to form segments a and b. Rotate point A 180 degrees around C to get A', and rotate point B 180 degrees around C to get B'. Measure angles ∠ACB' and ∠BCA', and draw line segment A'B'.
The prompt above was compiled from the original drawing commands and is for reference only.