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Investigation for Sum of Interior Angles of Polygons

Investigation for Sum of Interior Angles of Polygons
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2018-10-31 12:16
TrianglePolygonAngleGeometric ConstructionSlider Animation
This GeoGebra example dynamically constructs multiple polygons to visually demonstrate how the sum of interior angles changes with the number of sides. The core mathematical concept is the polygon interior angle sum formula (n-2)×180°, and the method of triangulating a polygon to derive this formula. Construction highlights: using the Polygon command to create polygons, Line and Segment commands for auxiliary lines, OrthogonalLine for perpendiculars, and Point/Intersect to define vertices and division points, effectively splitting polygons into triangles. Suitable for middle or high school geometry classes, this interactive investigation encourages students to discover the formula through hands-on exploration and inductive reasoning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(D, E, F, G) → poly2, d, e, f, g
  3. Polygon(H, I, J, K, L) → poly3, h, i, j, k, l
  4. Polygon(M, N, O, P, Q, R) → poly4, m, n, o, p, q, r
  5. Polygon(S, T, U, V, W, Z, A_1) → poly5, s, t, u, v, w, z_1, a_1
  6. Polygon(B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1) → poly6, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1
  7. Line(J_1, K_1) → j_1
  8. Line(L_1, M_1) → k_1
  9. OrthogonalLine(L_1, k_1) → l_1
  10. OrthogonalLine(K_1, j_1) → n_1
  11. OrthogonalLine(M_1, k_1) → p_1
  12. Point(j_1) → O_1
  13. Line(O_1, n_1) → q_1
  14. Line(J_1, q_1) → m_1
  15. Intersect(j_1, k_1) → N_1
  16. Intersect(p_1, m_1) → P_1
  17. Intersect(l_1, m_1) → Q_1
  18. Intersect(l_1, n_1) → R_1
  19. Intersect(p_1, n_1) → S_1
  20. Intersect(m_1, p_1) → T_1
  21. Intersect(l_1, m_1) → U_1
  22. Segment(Q_1, P_1) → r_1
  23. Segment(P_1, S_1) → s_1
  24. Segment(S_1, R_1) → t_1
  25. Segment(R_1, Q_1) → f_2
  26. Segment(J_1, K_1) → g_2
  27. Segment(L_1, M_1) → h_2
  28. Intersect(l_1, f_2) → V_1
  29. Intersect(q_1, l_1) → W_1
  30. Intersect(p_1, s_1) → Z_1
  31. Intersect(q_1, p_1) → A_2
  32. Segment(W_1, A_2) → i_2
  33. Segment(F, D) → j_2
  34. Segment(H, J) → k_2
  35. Segment(H, K) → l_2

AI Drawing Prompt Reference

Draw multiple polygons to show how the sum of interior angles changes as the number of sides increases, using auxiliary lines to divide the polygons into triangles, and explain the formula for the sum of interior angles of a polygon (n-2)×180° with the sum of angles in triangles. Start by drawing polygons with different numbers of sides, connect vertices with auxiliary lines to form triangles, and connect division points with line segments, finally showing the relationship between polygons and triangles.
The prompt above was compiled from the original drawing commands and is for reference only.