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Squares and Parallelograms on Triangle

Squares and Parallelograms on Triangle
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2017-07-27 05:05
TrianglePolygonTransformationGeometric ConstructionSlider Animation
This example demonstrates the construction of squares and parallelograms on a triangle. Key mathematical concepts include similarity transformation, similarity, slope difference, and general quadrilateral. Using GeoGebra commands such as Polygon, Segment, If, Line, Intersect, etc., various geometric objects such as polygons, segments, and rays are constructed. Suitable for middle school and above students to learn geometric construction and transformation.

GeoGebra Commands & Parameters

  1. Polygon(B, A, 4) → poly3, r, s, t, a, H, I
  2. Segment(A, B) → f
  3. Segment(B, C) → g
  4. Segment(C, A) → h
  5. Polygon(C, B, 4) → poly1, i, j, k, l, D, E
  6. Polygon(A, C, 4) → poly2, m, n_1, p, q, F, G
  7. If(t1 ≤ 1, Segment[B, B + (t1 * (D - B))], If[t1 ≤ 2, Segment[D, D + ((t1 - 1) * (E - D))], Segment[E, E + ((t1 - 2) * (C - E))]]) → e
  8. If(t1 ≤ 1, Segment[B, B + (t1 * (D - B))], If[t1 ≤ 2, Segment[D, D + ((t1 - 1) * (E - D))], Segment[E, E + ((t1 - 2) * (C - E))]]) → f_1
  9. If(t2 ≤ 1, Segment[C, C + (t2 * (F - C))], If[t2 ≤ 2, Segment[F, F + ((t2 - 1) * (G - F))], Segment[G, G + ((t2 - 2) * (A - G))]]) → i_1
  10. If(t3 ≤ 1, Segment[A, A + (t3 * (H - A))], If[t3 ≤ 2, Segment[H, H + ((t3 - 1) * (I - H))], Segment[I, I + ((t3 - 2) * (B - I))]]) → g_1
  11. Line(E, n_1) → b
  12. Line(F, e) → c
  13. Intersect(b, c) → J
  14. Line(H, i_1) → d
  15. Line(G, s) → h_1
  16. Intersect(d, h_1) → K
  17. Line(I, j) → j_1
  18. Line(D, g_1) → k_1
  19. Intersect(k_1, j_1) → L
  20. Segment(E, E + (t4 * (J - E))) → l_1
  21. Segment(F, F + (t4 * (J - F))) → m_1
  22. Segment(G, G + (t5 * (K - G))) → p_1
  23. Segment(H, H + (t5 * (K - H))) → q_1
  24. Segment(I, I + (t6 * (L - I))) → r_1
  25. Segment(D, D + (t6 * (L - D))) → s_1
  26. Ray(L, B) → t_1
  27. Ray(K, A) → a_1
  28. Midpoint(F, A) → Q
  29. Midpoint(H, B) → R
  30. Midpoint(D, C) → S
  31. Segment(L, L + (t7 * (Q - L))) → d_1
  32. Segment(J, J + (t7 * (R - J))) → c_1
  33. Intersect(d_1, c_1) → M
  34. Segment(K, K + (t7 * (S - K))) → b_1

AI Drawing Prompt Reference

Construct a triangle, then build squares outward on each of its three sides. On each square, attach a parallelogram whose outer vertex can slide along the square's perimeter using three separate sliders. Connect the outer vertices of the parallelograms to form three intersection points, and draw rays from these points to the triangle's vertices. Finally, take midpoints of certain segments, connect them to the intersection points, and find new intersections, creating a complex geometric figure with triangles, squares, parallelograms, segments, rays, and points.
The prompt above was compiled from the original drawing commands and is for reference only.