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Trapezoid Mid-Segment Exploration

Trapezoid Mid-Segment Exploration
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2017-03-16 00:06
PolygonTrigonometryGeometric Construction
This example demonstrates the properties of a trapezoid's mid-segment, showing it is parallel to the bases and equal to half the sum of the base lengths. Key math concepts include trapezoids, mid-segments, parallel lines, and segment lengths. It is constructed using GeoGebra commands like Ray, Segment, Line, Point, Polygon, Midpoint, Rotate, Circle, Intersect, CircleSector, Dilate, Vector, and Translate. Suitable for middle school and above students to visually understand geometric properties.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Segment(A, B) → b
  3. Line(C, b) → c
  4. Point(c) → D
  5. Ray(C, D) → d
  6. Point(d) → E
  7. Segment(C, A) → e
  8. Segment(C, E) → f
  9. Segment(E, B) → g
  10. Polygon(A, B, E, C) → poly1, a_1, b_1, e_1, c_1
  11. Midpoint(e) → F
  12. Midpoint(g) → G
  13. Segment(F, G) → h
  14. Rotate(A, (-α), G) → A'
  15. Rotate(B, (-α), G) → B'
  16. Rotate(E, (-α), G) → E'
  17. Rotate(C, (-α), G) → C'
  18. Polygon(A', B', E', C') → poly1', a', b', e', c'
  19. Rotate(F, (-α), G) → F'
  20. Rotate(G, (-α), G) → G'
  21. Segment(F', G') → h'
  22. Segment(B', A') → i
  23. Segment(A', C') → j
  24. Segment(C', E') → k
  25. Segment(E', B') → l
  26. Segment(C, F) → m
  27. Segment(F, A) → n
  28. Segment(E, G) → p
  29. Segment(G, B) → q
  30. Segment(C', F') → r
  31. Segment(F', A') → s
  32. Line(C, A) → t
  33. Circle(F, 1) → f_1
  34. Intersect(f_1, h, 1) → J
  35. Intersect(t, m) → K
  36. Intersect(t, m) → L
  37. Intersect(f_1, t) → M, N
  38. CircleSector(F, J, M) → h_1
  39. Dilate(F, 1 - o, A) → F'_1
  40. Dilate(F, 1 - o, C) → F'_2
  41. Vector(F, F'_2) → u
  42. Vector(F, F'_1) → v
  43. Translate(h_1, v) → k_1
  44. Translate(h_1, u) → p_1
  45. Dilate(F, If[0 < w ≤ 1, 1 - w, 0], C) → F'_3
  46. Vector(F, F'_3) → u_1
  47. Translate(G, u_1) → G'_1
  48. Segment(F'_3, G'_1) → d_1
  49. Dilate(F, If[1 < w ≤ 2, 2 - w, 0], C) → F'_4
  50. Vector(F, F'_4) → v_1
  51. Translate(F', v_1) → F''
  52. Translate(G, v_1) → G'_2
  53. Segment(G'_2, F'') → g_1