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Pythagorean Theorem and Median Line Test

Pythagorean Theorem and Median Line Test
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2016-05-10 17:10
TriangleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the Pythagorean theorem and the properties of the median line in a triangle. By constructing a right triangle and its median, it uses distance, angles, and circles to illustrate the properties of the median line. GeoGebra commands such as Segment, Semicircle, Distance, Polygon, Angle, and OrthogonalLine are utilized. Suitable for middle school and above students to learn geometry and trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → a
  2. Semicircle(A_1, B_1) → c
  3. Distance(A_1, C) → b
  4. Polygon(A_1, C, B_1) → ABC, AC, CB, BA
  5. Angle(A_1, C, B_1) → α
  6. Angle(B_1, A_1, C) → β
  7. Angle(A_1, C, B_1) → γ
  8. Angle(C, B_1, A_1) → δ
  9. OrthogonalLine(C, CB) → D_1
  10. OrthogonalLine(B_1, CB) → E_1
  11. Circle(C, B_1) → F_1
  12. Intersect(F_1, D_1, 2) → D
  13. Line(D, CB) → d
  14. Intersect(E_1, d) → E_2
  15. Intersect(d, D_1) → G
  16. Intersect(E_1, d) → E
  17. Polygon(C, D, E_2, B_1) → CBED, c_1, d_1, e_2, b_1
  18. OrthogonalLine(C, AC) → e
  19. OrthogonalLine(A_1, AC) → f
  20. Circle(A_1, C) → F
  21. Intersect(F, f) → H, I
  22. Line(I, AC) → g
  23. Intersect(e, g) → J
  24. Polygon(I, A_1, C, J) → ACJL, i, a_1, c_2, j
  25. OrthogonalLine(A_1, BA) → k
  26. OrthogonalLine(B_1, BA) → h
  27. Circle(B_1, A_1) → p
  28. Intersect(p, h) → K, L
  29. Line(L, BA) → l
  30. Intersect(k, l) → M
  31. Polygon(A_1, B_1, L, M) → poly1, a_2, b_2, l_1, ABLM
  32. Polygon(A_1, B_1, L, M) → poly2, a_3, b_3, l_2, m
  33. Midpoint(A_1, J) → N
  34. Midpoint(B_1, G) → O
  35. Intersect(l_2, m) → P
  36. Midpoint(P, B_1) → B_2
  37. Semicircle(A_1, B_1) → q_1
  38. Intersect(AC, CB) → A

AI Drawing Prompt Reference

Draw a right triangle with its hypotenuse and legs. Mark the midpoints of the hypotenuse and legs, and connect the midpoint of the hypotenuse to the right angle vertex to form the median. Use circles and perpendicular lines to illustrate the median theorem, label the angles and side lengths, and finally draw the quadrilateral formed by the intersection points of the median and circles.
The prompt above was compiled from the original drawing commands and is for reference only.