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Angles in Tangram

Angles in Tangram
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2023-10-02 14:41
TrianglePolygonAngleTransformation
In collections MateTangram
This example explores the measures of angles in the Tangram pieces. Key mathematical concepts include geometry, isosceles triangles, parallelograms, right triangles, and squares. Commands used include Polygon, Segment, Midpoint, Line, Intersect, Rotate, and InteriorAngles. Suitable for high-grade elementary to junior high school students to learn about geometric shapes and angles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poli1, frame3, frame4, frame1, frame2, C, D
  2. Segment(A, C) → frame12
  3. Midpoint(D, C) → E
  4. Midpoint(D, A) → F
  5. Segment(F, E) → frame5
  6. Midpoint(A, C) → G
  7. Segment(B, G) → frame9
  8. Midpoint(F, E) → H
  9. Midpoint(G, C) → I
  10. Segment(H, I) → frame7
  11. Segment(G, H) → frame8
  12. Line(F, frame8) → j
  13. Intersect(j, frame12) → J
  14. Segment(F, J) → frame11
  15. Polygon(A, G, B) → poli2, b_1, a_1, g_1
  16. Rotate(O + (a_1, 0), Angle[B - G] + Angle[O - N] - Angle[G - A], O) → P
  17. Polygon(N, O, P) → poli4, p, n, o
  18. Polygon(B, G, C) → poli3, c_1, b_2, g_2
  19. Rotate(L + (b_2, 0), Angle[C - G] + Angle[L - K] - Angle[G - B], L) → M
  20. Polygon(K, L, M) → poli5, m, k_1, l
  21. Polygon(H, E, C, I) → poli6, h_1, e_1, c_2, i_1
  22. Rotate(R + (e_1, 0), Angle[C - E] + Angle[R - Q] - Angle[E - H], R) → S
  23. Rotate(S + (c_2, 0), Angle[I - C] + Angle[S - R] - Angle[C - E], S) → T
  24. Polygon(Q, R, S, T) → poli7, q, r, s, t
  25. Polygon(H, G, I) → poli8, i_2, h_2, g_3
  26. Rotate(V + (h_2, 0), Angle[I - G] + Angle[V - U] - Angle[G - H], V) → W
  27. Polygon(U, V, W) → poli9, w, u, v
  28. Polygon(F, H, G, J) → poli10, f_1, h_3, g_4, j_1
  29. Rotate(A_1 + (h_3, 0), Angle[G - H] + Angle[A_1 - Z] - Angle[H - F], A_1) → B_1
  30. Rotate(B_1 + (g_4, 0), Angle[J - G] + Angle[B_1 - A_1] - Angle[G - H], B_1) → C_1
  31. Polygon(Z, A_1, B_1, C_1) → poli11, z, a_2, b_3, c_3
  32. Polygon(F, J, A) → poli12, a_3, f_2, j_2
  33. Rotate(E_1 + (f_2, 0), Angle[A - J] + Angle[E_1 - D_1] - Angle[J - F], E_1) → F_1
  34. Polygon(D_1, E_1, F_1) → poli13, f_3, d_1, e_2
  35. Polygon(F, D, E) → poli14, e_3, f_4, d_2
  36. Rotate(H_1 + (f_4, 0), Angle[E - D] + Angle[H_1 - G_1] - Angle[D - F], H_1) → I_1
  37. Polygon(G_1, H_1, I_1) → poli15, i_3, g_5, h_4
  38. InteriorAngles(poli7) → parA, parB, parC, parD
  39. InteriorAngles(poli11) → quaA, quaB, quaC, quaD
  40. InteriorAngles(poli5) → triGA, triGB, triGC
  41. InteriorAngles(poli4) → triVA, triVB, triVC
  42. InteriorAngles(poli15) → triAA, triAB, triAC
  43. InteriorAngles(poli9) → triRA, triRB, triRC
  44. InteriorAngles(poli13) → triPUC, triPUA, triPUB

AI Drawing Prompt Reference

Draw a tangram-style angle study figure made of several connected polygons on the same plane. Start by constructing an outer outline using a few triangles and quadrilaterals sharing common points. Then take midpoints of selected sides, connect the relevant midpoint-to-midpoint pairs with segments to create internal subdivisions. Next, repeatedly rotate the small polygon pieces around specified centers so that they align into distinct triangular and quadrilateral regions, forming one larger connected quadrilateral area as well. Finish by labeling the interior angle measures for each of the resulting quadrilaterals and triangles, so the angles can be compared.
The prompt above was compiled from the original drawing commands and is for reference only.