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Trig Ratios of Similar Right Triangles by Ben Dougherty

Trig Ratios of Similar Right Triangles by Ben Dougherty
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2014-06-28 02:42
TriangleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates comparing trigonometric ratios between a triangle and its dilated version using a slider to control the scale factor. Core concepts include trigonometry, similar triangles, and dilation transformations. Constructed using Polygon, Angle, and Dilate commands with objects like A, B, C, poly1, c, a, b, α, β, k, A', B', C', etc. Ideal for high school students to explore the relationship between similar triangles and trigonometric ratios, and the application of geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(A, B, C) → α
  3. Angle(B, C, A) → β
  4. Dilate(A, k, A) → A'
  5. Dilate(B, k, A) → B'
  6. Dilate(C, k, A) → C'
  7. Polygon(A', B', C') → poly1', c', a', b'
  8. Angle(A, B', C') → γ
  9. Angle(B', C', A) → δ

AI Drawing Prompt Reference

Draw a right triangle with three vertices, marking its two acute angles. Using one vertex as the center of dilation, apply a scale factor controlled by a slider to enlarge or shrink the triangle, producing a similar triangle with corresponding sides parallel and angles equal. In the new triangle, mark the angle opposite the dilation center and the angle adjacent to it. Use distinct colors or line styles for the original and dilated triangles, and include a slider to dynamically show that the trigonometric ratios of corresponding acute angles remain unchanged.
The prompt above was compiled from the original drawing commands and is for reference only.