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Isosceles Right Triangle Exploration

Isosceles Right Triangle Exploration
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2019-02-25 06:27
TriangleCircleCalculusTransformationGeometric Construction
This example demonstrates the properties and transformations of an isosceles right triangle. It involves core concepts like isosceles triangles, right triangles, similarity transformation, equations, circumcircle, definite integral, and differential calculus. Construction highlights include using GeoGebra commands such as Sequence, Segment, Circle, OrthogonalLine, Intersect, Dilate, Rotate, Angle, and Polygon. Suitable for high school mathematics teaching, focusing on geometric construction and concept comprehension.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[(1, 0), i°, (0, 0)], i, 15, 360, 15) → list1
  2. Segment(B, A) → g
  3. Circle(B, A) → h
  4. OrthogonalLine(B, g) → i
  5. Intersect(h, i) → I, J
  6. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], A) → G'
  7. Segment(B, G') → k
  8. Rotate(B, If[1 < j ≤ 2, ((j - 1) * π / 2), π / 2], B) → G'_1
  9. Rotate(G', If[1 < j ≤ 2, ((j - 1) * π / 2), π / 2], B) → C
  10. Segment(G'_1, C) → k'
  11. Angle(A, B, C) → α
  12. Dilate(J, If[2 < j ≤ 3, 3 - j, 0], A) → J'
  13. Segment(J, J') → l
  14. Polygon(B, A, J) → poly2, j_1, g_1, h_1