MathPlotAI Logo MathPlotAI

Dynamic Construction of Squares and Parallelograms on a Triangle

Dynamic Construction of Squares and Parallelograms on a Triangle
Loading the math board and drawing, please wait…
2017-07-27 05:16
TrianglePolygonGeometric ConstructionSlider Animation
This GeoGebra example demonstrates the dynamic construction of squares erected externally on the three sides of a triangle, together with associated parallelograms derived from the triangle's vertices and side points. Core mathematical concepts include triangles, squares, parallelograms, polygon properties, and planar geometric relationships such as intersection, midpoint, perpendicularity, and symmetry. The construction is based on GeoGebra commands Polygon, Segment, If, Line, Intersect, Ray, and Midpoint, involving polygon objects poly1, poly2, poly3 and point objects A, B, C, D, E, F, G, H, I, with Reset and Slide buttons for animation. It is suitable for middle school and high school plane geometry instruction, classroom demonstrations, and independent exploration of 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, G) → Q
  29. Midpoint(H, I) → R
  30. Midpoint(D, E) → 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