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Three Similar Triangles

Three Similar Triangles
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2016-05-04 22:32
TriangleAngleGeometric Construction
This example demonstrates the properties of three similar triangles. By constructing similar triangles, you can observe that their corresponding angles are equal and their corresponding sides are proportional. Using GeoGebra commands such as Point, Semicircle, Polygon, etc., it is convenient to perform geometric constructions. Suitable for middle and high school students to learn about similar triangles.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Polygon(C, A, B) → poly1, b, c_1, a
  6. Polygon(C, D, B) → poly2, b_1, c_2, d
  7. Polygon(C, D, A) → poly3, a_1, c_3, d_1
  8. Circle(E, Distance[A, D]) → e
  9. Point(e) → F
  10. Segment(E, F) → f
  11. OrthogonalLine(F, f) → g
  12. Circle(E, Distance[A, C]) → h
  13. Intersect(h, g) → G, H
  14. Segment(E, H) → i
  15. Segment(F, H) → j
  16. Circle(I, Distance[B, D]) → k
  17. Point(k) → J
  18. Segment(I, J) → l
  19. OrthogonalLine(J, l) → m
  20. Circle(I, Distance[B, C]) → p
  21. Intersect(p, m) → K, L
  22. Segment(K, I) → n
  23. Segment(J, K) → q
  24. Angle(E, H, F) → α
  25. Angle(A, C, D) → β
  26. Angle(J, K, I) → γ
  27. Angle(D, C, B) → δ
  28. Angle(C, D, A) → ε
  29. Angle(B, D, C) → ζ
  30. Angle(H, F, E) → η
  31. Angle(I, J, K) → θ
  32. Segment(C, D) → r
  33. Polygon(E, F, H) → poly3copy, h_1, e_1, f_1
  34. Polygon(J, I, K) → poly2copy, k_1, j_1, i_1
  35. Distance(E, K) → EK
  36. Distance(B, C) → BC
  37. Distance(I, K) → IK
  38. Distance(A, B) → AB

AI Drawing Prompt Reference

Draw three similar triangles. Start by taking points A and B on the x-axis, draw a semicircle with A and B as the diameter, and take point C on the semicircle. Connect A, B, and C to form triangle ABC. Then, take point D on the semicircle, draw a circle with radius AD, and take the intersection of the circle with the diameter AB as point E. Draw the perpendicular line to EF, and draw a circle with radius AC, intersecting the perpendicular line at point F. Connect E, F, and H to form triangle EFG. Repeat the above steps with BD as the radius to draw a circle intersecting the perpendicular line at point J, and connect I, J, and K to form triangle IJK. Finally, measure the lengths and angles to observe the properties of similar triangles.
The prompt above was compiled from the original drawing commands and is for reference only.