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Trig Ratios of Similar Right Triangles

Trig Ratios of Similar Right Triangles
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2015-11-17 22:28
TriangleTrigonometryGeometric Construction
This example demonstrates how to compare trigonometric ratios between a triangle and its dilated version using a slider to control the scale factor. Core concepts include trigonometry, similar triangles, and geometric transformations (dilation). Construction involves Polygon, Angle, and Dilate commands, with text elements to display ratios and angles. Ideal for high school students to explore the invariance of trig ratios under similarity transformations and the integration of geometric constructions with dynamic demonstrations.

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