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Exterior Angles of Polygons by Adam Wolfe

Exterior Angles of Polygons by Adam Wolfe
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2019-05-22 08:08
PolygonAngle
This example demonstrates the properties of exterior angles in polygons. Key mathematical concepts include the relationship between exterior and interior angles. Using GeoGebra commands such as Polygon, Angle, and Vector, it dynamically shows that the sum of exterior angles in any polygon is always 360 degrees. Suitable for middle school and above students to learn geometric construction and exterior angle theorems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d_1
  2. Polygon(E, G, H, F) → poly2, e, g, h, f_1
  3. Sequence(Circle[(0, ((-d)) / 2), ((t - i) * λ)], i, 0, 1000) → list1
  4. Sequence(Circle[(0, d / 2), ((t - i) * λ)], i, 0, 1000) → list1_1
  5. Angle(J, K, J') → α
  6. Mirror(J', xAxis) → J''
  7. Ray(K, J') → i
  8. Mirror(K, xAxis) → K'
  9. Mirror(J', xAxis) → J''_1
  10. Ray(K', J''_1) → i'
  11. Polygon(L, M, N, O) → poly3, l, m, n, o
  12. Textfield(nm) → InputBox1
  13. Textfield(d) → InputBox2
  14. Sequence(Segment[(10, (10 * tan(asin((mmm * λ / d))))), (0, 0)], mmm, -10, 10) → L_2
  15. Sequence(Segment[(10, (10 * tan(asin((mmm * λ / d))))), (10.2, (10 * tan(asin((mmm * λ / d)))))], mmm, -10, 10) → L_1
  16. Sequence(Segment[(10, lll), (10.2, lll)], lll, -10, 10, 1) → L_3
  17. Sequence(Segment[(10, lll), (10.1, lll)], lll, -10, 10, 0.2) → L_4
  18. Polygon((0, -4), (19.95, -4), (19.95, -10), (0, -10)) → q1, p, q, r, s
  19. Vector((0, -4.2), (10, -4.2)) → u
  20. Vector((10, -4.2), (0, -4.2)) → v
  21. Vector((-0.4, ((-d)) / 2), (-0.4, d / 2)) → w
  22. Vector((-0.4, d / 2), (-0.4, ((-d)) / 2)) → u_1
  23. Polygon((0, 4), (19.95, 4), (19.95, 10), (0, 10)) → q2, h_1, i_1, j_1, k_1
  24. Segment((10, spread2), (12, spread2)) → m_1
  25. Segment((10, (-spread) - 4), (12, (-spread) - 4)) → g_1
  26. Segment((10, 0), (12, 0)) → l_1

AI Drawing Prompt Reference

Draw a polygon to demonstrate the relationship between exterior and interior angles. Dynamically display multiple polygons' exterior angles and prove their sum is always 360 degrees. Use circles and rays to construct exterior angles, and show angle symmetry through mirroring and vector tools. Finally, input side lengths and angles in text boxes to draw dynamic sides and angles, completing the geometric proof.
The prompt above was compiled from the original drawing commands and is for reference only.