MathPlotAI Logo MathPlotAI

Tangram Side Lengths: Pythagorean Theorem Application

Tangram Side Lengths: Pythagorean Theorem Application
Loading the math board and drawing, please wait…
2023-10-01 19:15
TrianglePolygonTrigonometryCoordinate GeometryGeometric Construction
In collections MateTangram
This example demonstrates how to calculate the side lengths of all seven pieces in a Tangram puzzle. By setting the square's side length as unit 1, the Pythagorean theorem is applied to find the leg and hypotenuse lengths of large, small, and medium triangles, as well as the side relationships of parallelograms and the square. Construction uses GeoGebra commands: Polygon for drawing polygons, Segment for labeling sides, Line for auxiliary lines, Intersect for finding intersections, Rotate for piece rotation and assembly, and Midpoint for locating midpoints. Core math concepts include right triangle leg-hypotenuse relationships, isosceles triangle properties, parallelogram opposite side equality, and square angle-side relationships. Ideal for middle school students learning the Pythagorean theorem and for geometry teachers demonstrating mathematical principles behind Tangram puzzles.

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

AI Drawing Prompt Reference

Draw a square frame, then use the Pythagorean theorem to calculate the side lengths of large, small, and medium triangles, as well as the side relationships of parallelograms and the square. Start by drawing the square frame, then draw auxiliary lines and midpoints, and finally construct each piece of the tangram puzzle through rotation and midpoint construction.
The prompt above was compiled from the original drawing commands and is for reference only.