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Properties of Isosceles Triangles by Drew Lazar

Properties of Isosceles Triangles by Drew Lazar
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2019-07-06 02:32
TriangleFunctionCoordinate Geometry
In collections Exploring Feyman's Triangle
This example demonstrates the properties of isosceles triangles, including their definition and related function graphs. Using GeoGebra commands such as Segment, Dilate, and Intersect, isosceles triangles are constructed and their properties are observed. Suitable for middle school and above students to learn geometric construction and function graphs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(C, B) → g
  3. Segment(A, C) → h
  4. Dilate(C, 1 / 3, A) → C'
  5. Dilate(A, 1 / 3, B) → A'
  6. Dilate(B, 1 / 3, C) → B'
  7. Segment(B, C') → i
  8. Segment(A, B') → j
  9. Segment(A', C) → k
  10. Intersect(k, i) → E
  11. Intersect(j, i) → D
  12. Intersect(k, j) → F
  13. Polygon(B, A, C) → t1, c, b, a
  14. Polygon(E, D, F) → t2, f_1, d, e
  15. Polygon(B, E, F, B') → q2, b_1, d_2, f_2, b'
  16. Polygon(F, D, C', C) → q3, f_3, e_2, c', c_1
  17. Polygon(B, A', E) → t3, d_3, b_2, l
  18. Polygon(D, A, C') → t4, m, e_3, a_2
  19. Polygon(B', F, C) → t5, c_2, n, f_4
  20. FractionText(q3 / t1) → text8
  21. Polygon(E, A', A, D) → q1, e_1, a', a_1, d_1
  22. FractionText(q2 / t1) → text10
  23. FractionText(q1 / t1) → text12
  24. FractionText(t3 / t1) → text14
  25. FractionText(t3 / t1) → text16
  26. FractionText(t4 / t1) → text18
  27. PointIn(q1) → G
  28. PointIn(t3) → H
  29. PointIn(q2) → I
  30. PointIn(t2) → J
  31. PointIn(t4) → K
  32. PointIn(q3) → L
  33. PointIn(t5) → M

AI Drawing Prompt Reference

Draw an isosceles triangle. Mark points on each side at one-third from a vertex, and connect them to form an inner triangle. Then draw segments from each original vertex to the opposite side's trisection point, creating intersections that divide the interior into several smaller triangles and quadrilaterals. Shade or color these regions distinctly, and label each region with its fractional area relative to the whole triangle. The figure should show a symmetric subdivision, illustrating properties of isosceles triangles.
The prompt above was compiled from the original drawing commands and is for reference only.