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Demonstrate Vertical Angles Are Equal

Demonstrate Vertical Angles Are Equal
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2013-02-21 06:34
AngleGeometric ConstructionSlider Animation
In collections Introduction to Geometry
This example demonstrates the property that vertically opposite angles are equal. It involves core math concepts like vertical angles, angle measurement, and geometric transformations. Constructed using commands such as Line, Point, Segment, Angle, Polygon, Rotate in GeoGebra. Suitable for middle school students and above to learn geometric transformations and angle relationships, or for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Line(B, A) → a
  2. Line(C, A) → b
  3. Point(a) → D
  4. Segment(B, D) → c
  5. Point(b) → E
  6. Segment(C, E) → d
  7. Angle(B, A, C) → α
  8. Angle(E, A, B) → β
  9. Angle(D, A, E) → γ
  10. Angle(C, A, D) → δ
  11. Polygon(C, A, B) → poly1, b_1, c_1, a_1
  12. Polygon(B, A, E) → poly2, e, b_2, a_2
  13. Rotate(C, -red, A) → C'
  14. Rotate(A, -red, A) → A'
  15. Rotate(B, -red, A) → B'
  16. Polygon(C', A', B') → poly1', b', c', a'
  17. Rotate(B, -green, A) → B'_1
  18. Rotate(A, -green, A) → A'_1
  19. Rotate(E, -green, A) → E'
  20. Polygon(B'_1, A'_1, E') → poly2', e', b'_1, a'_1
  21. Angle(E', A, B'_1) → ζ
  22. Angle(B', A, C') → ε

AI Drawing Prompt Reference

Draw two intersecting lines to form four angles. Mark the vertex and sides of one angle and measure its size. Take points on each line and connect them to form two triangles. Rotate one triangle so that its vertex aligns with the original angle's vertex, observing the relationship between the rotated and original triangles. Measure the angles of the rotated triangle and compare them with the original angles to demonstrate that vertical angles are equal.
The prompt above was compiled from the original drawing commands and is for reference only.