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M-Machine Construction and Proof Using Similar Triangles

M-Machine Construction and Proof Using Similar Triangles
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2015-12-14 09:54
TriangleAngleGeometric Construction
This example demonstrates the construction and proof of M-Machine using the properties of similar triangles. Key mathematical concepts include similar triangles, triangles, angles, and ratios. Using GeoGebra commands such as Point, Intersect, Segment, and Polygon, multiple geometric objects are constructed. Suitable for students at the middle school level and above for geometric construction and proof.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. OrthogonalLine(A, a) → b
  3. Intersect(a, b) → B
  4. Segment(B, A) → c
  5. Line((0, 0), B) → d
  6. Point(xAxis) → C
  7. Intersect(e, f) → D
  8. Segment(D, C) → g
  9. Intersect(h, d) → E
  10. OrthogonalLine(E, xAxis) → i
  11. Intersect(i, xAxis) → F
  12. Segment(E, F) → j
  13. Segment(D, E) → k
  14. Polygon(B, G, A) → poly1, a_1, b_1, g_1
  15. Polygon(E, G, F) → poly2, f_1, e_1, g_2
  16. Angle(B, A, G) → α
  17. Angle(D, C, G) → β
  18. Angle(E, F, G) → γ
  19. Angle(A, G, B) → δ
  20. Angle(F, G, E) → ε