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Pythagorean Polygons

Pythagorean Polygons
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2014-10-12 18:58
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the Pythagorean theorem through polygons, helping students understand the relationship between the area of polygons and dependent variables. Using commands like Segment, OrthogonalLine, Point, Polygon, Centroid, and Angle, students can explore the properties of polygons. Suitable for middle school and above students to learn about polygons and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Polygon(C, B, A) → poly1, a_1, c, b_1
  5. Polygon(C, B, Sides) → poly2, d, p_1, s_1, b_2, D, G, J, M, P, S, V, e, A_1, D_1, G_1, f, m, r, c_1, f_1, i_1, l_1
  6. Polygon(A, C, Sides) → poly3, g, q_1, t_1, c_2, E, H, K, N, Q, T, W, h, B_1, E_1, H_1, i, p, s, d_1, g_1, j_1, m_1
  7. Polygon(B, A, Sides) → poly4, j, r_1, a_2, d_2, F, I, L, O, R, U, Z, k, C_1, F_1, I_1, l, q, t, e_1, h_1, k_1, n_1
  8. Centroid(poly2) → J_1
  9. Centroid(poly3) → K_1
  10. Centroid(poly4) → L_1
  11. Angle(B, A, C) → α
  12. Segment(C, A) → e_2
  13. Segment(A, B) → f_2
  14. Segment(C, B) → g_2

AI Drawing Prompt Reference

Draw a right triangle ABC with point A at the origin, point B on the x-axis, and point C on the y-axis. Construct a square using points A, B, and C as starting points, then find the centroids of each square. Measure the angle BAC.
The prompt above was compiled from the original drawing commands and is for reference only.