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Properties of Isosceles Trapezoid

Properties of Isosceles Trapezoid
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2020-10-21 00:49
PolygonVectorGeometric Construction
This example demonstrates the properties of an isosceles trapezoid, including its definition, midsegment theorem, and area formula. Using GeoGebra commands such as Point, Vector, and Segment, the trapezoid is constructed and geometric constructions are performed. Suitable for middle and high school students to learn geometry and algebra.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_x
  2. Textfield(m) → inputBox1
  3. Textfield(s) → inputBoxf
  4. Point(i) → K
  5. Vector(K, s_{inv}D) → w
  6. Vector(s_{inv}D, m_{invSinvD}) → z
  7. Vector(m_{invSinvD}, q_{inv+}) → d
  8. Vector(m_{invSinvD}, q_{inv-}) → f
  9. Vector(q_{inv+}, I) → h_1
  10. Vector(q_{inv-}, J) → j
  11. Textfield(h) → inputBox2
  12. Textfield(b) → inputBox3
  13. Textfield(m_*) → inputBox4
  14. Textfield(m) → inputBox5
  15. Textfield(s) → inputBox6
  16. Point(i) → T_1
  17. Vector(T_1, S_*) → w_1
  18. Vector(S_*, T_*) → u_2
  19. Vector(T_*, R_1) → v_2
  20. Vector(T_*, R_2) → w_2
  21. Vector(R_1, R_#) → a_2
  22. Vector(R_2, R_*) → b_2
  23. Sequence(h - num, h + num) → N
  24. Zip(Vector[(0, i), (2, R(i))], i, N) → QuadRvlist
  25. Zip(Vector[(2, R(i)), (4, q(R(i)))], i, N) → Quadqvlist
  26. Zip(Vector[(4, q(R(i))), (6, m(q(R(i))))], i, N) → Quadmvlist
  27. Zip(Vector[(6, m(q(R(i)))), (8, s(m(q(R(i)))))], i, N) → Quadgvlist
  28. Point(i) → A
  29. Ray(T_1, T_1 + (0, 1)) → g
  30. Ray(S_*, S_* + (0, 1)) → k
  31. Ray(T_*, T_* + (0, m_*)) → p
  32. Ray(R_1, R_1 + (0, 1)) → r
  33. Ray(R_2, R_2 - (0, 1)) → t
  34. Ray(R_#, R_# + (0, 1)) → f_1
  35. Ray(R_*, R_* - (0, 1)) → g_1
  36. Segment(R_1, R_2) → i_1
  37. Segment(R_#, R_*) → j_1

AI Drawing Prompt Reference

Draw an isosceles trapezoid to demonstrate its midsegment theorem and area formula. Start by sketching the bases and top, then determine the lengths of the legs. Label the midsegment and use vectors to construct the trapezoid's vertices and sides. Highlight key points and midsegment length with distinct colors. Finally, perform geometric constructions to show that the midsegment equals half the sum of the bases, ensuring clarity and educational value.
The prompt above was compiled from the original drawing commands and is for reference only.