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Length Ratios in Similar Triangles by Luis Alberto

Length Ratios in Similar Triangles by Luis Alberto
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2018-05-29 10:43
TriangleTransformationGeometric ConstructionSlider Animation
① This GeoGebra applet demonstrates that corresponding side lengths of similar triangles maintain a constant ratio, allowing users to drag vertices and observe the invariant proportion. ② Core mathematical concepts include similarity of triangles, the property of proportional corresponding sides, and geometric transformations such as rotation and dilation (homothety). ③ Construction highlights: using GeoGebra commands like Rotate, Dilate, Polygon, and Distance, the applet creates two similar triangles (original ABC and transformed A'B'C'), measures side lengths (a, b, c, a', b', c'), and displays the ratios via text objects (text1–text6). Auxiliary points D, E, F and variables like distanceAB, distanceBC, distanceAC support the measurements. ④ Suitable for middle-to-high school geometry classes, this interactive tool helps students grasp the side-ratio theorem of similar triangles and can be used for teacher demonstrations or self-guided exploration.

GeoGebra Commands & Parameters

  1. Rotate(A_1, α, B) → A'
  2. Angle(A_1, B, A') → β
  3. Polygon(B, C_1, A') → poly1, a', b_1, c
  4. Dilate(B, Enlarge, B) → B'
  5. Dilate(C_1, Enlarge, B) → C
  6. Dilate(A', Enlarge, B) → A
  7. Polygon(B', C, A) → poly1', a'', b', c'
  8. Distance(A, C) → distanceAC
  9. Midpoint(A, C) →
  10. Distance(B, C) → distanceBC
  11. Midpoint(B, C) →
  12. Midpoint(b') → D
  13. Midpoint(a'') → E
  14. Midpoint(c') → F
  15. Distance(A, B) → distanceAB
  16. Midpoint(A, B) →

AI Drawing Prompt Reference

Draw two similar triangles ABC and A'B'C'. First, rotate point B around point A to get point A'. Then, rotate point C around point B to get point C'. Next, enlarge point A around point B to get point A', enlarge point C around point B to get point C', and enlarge point A' around point B to get point A'. Draw triangle A'B'C'. Measure the lengths of sides AB, BC, AC, A'B', B'C', and A'C' in triangles ABC and A'B'C'. Find the midpoints of sides AB and A'B' (D and D'), BC and B'C' (E and E'), and AC and A'C' (F and F') in triangles ABC and A'B'C'. Display the ratios of the lengths of AB and A'B', BC and B'C', and AC and A'C'.
The prompt above was compiled from the original drawing commands and is for reference only.