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Triangle with Equal Area and Perimeter

Triangle with Equal Area and Perimeter
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2016-04-30 23:51
Triangle
This example demonstrates that for any triangle, there exists a similar triangle such that its area and perimeter are numerically equal. Key concepts include similar triangles, area, and perimeter. The construction uses GeoGebra commands such as Polygon, Dilate, and PointIn. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A_1, B, C) → a_1, c, a_2, b
  2. Dilate(A_1, d, D) → A'
  3. Dilate(B, d, D) → B'
  4. Dilate(C, d, D) → C'
  5. Polygon(A', B', C') → a, c', a', b'
  6. PointIn(a) → Pointpoly1'_1
  7. Perimeter(a) → p
  8. PointIn(a) → Pointpoly1'
  9. Perimeter(a_1) → p_1
  10. PointIn(a_1) → Pointpoly1
  11. PointIn(a_1) → Pointa1
  12. Intersect(f, g) → E, F
  13. Textfield(d) → inputBox1