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Ratios in Right Triangles by omirontchik

Ratios in Right Triangles by omirontchik
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2018-02-28 23:55
TriangleTrigonometryCoordinate Geometry
This example demonstrates the ratio relationships in right triangles. Key mathematical concepts include triangles, right triangles, angles, and ratios. Using GeoGebra commands such as Segment, OrthogonalLine, Point, Polygon, and Dilate, the construction of right triangles and the observation of ratio changes are illustrated. Suitable for students at the junior high school level and above to learn trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(A, C) → c
  5. Segment(C, B) → d
  6. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  7. Dilate(A, 0.23, D) → I
  8. Dilate(C, 0.23, D) → K
  9. Dilate(B, 0.23, D) → J
  10. Polygon(I, K, J) → poly1', b', a', c'
  11. Dilate(A, 0.68, E) → H
  12. Dilate(C, 0.68, E) → F
  13. Dilate(B, 0.68, E) → G
  14. Polygon(H, F, G) → poly1'_1, b'_1, a'_1, c'_1
  15. Segment(J, K) → e
  16. Angle(K, J, I) → α
  17. Angle(F, G, H) → β
  18. Angle(C, B, A) → γ
  19. LaTeX(f, true, true) → text3
  20. Angle(J, I, K) → δ
  21. Angle(G, H, F) → ε
  22. Angle(B, A, C) → ζ

AI Drawing Prompt Reference

Draw a right triangle ABC with A as the right angle. Construct a perpendicular line to AB through B, intersecting at C. Connect AC and BC to form the triangle. Then, using point D as the center, dilate the triangle ABC by 0.23 and 0.68 to create two new triangles. Measure and display the angles of the triangles.
The prompt above was compiled from the original drawing commands and is for reference only.