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Similarity Transformation and Isosceles Triangle Construction

Similarity Transformation and Isosceles Triangle Construction
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2015-04-24 13:28
TriangleTransformationGeometric Construction
In collections Geometry of Angles (Student Created)
This example demonstrates the process of constructing similar triangles through rotation transformation. It involves core mathematical concepts such as rational numbers, similarity transformation, plane figures, isosceles triangles, and area calculation. The construction uses GeoGebra commands like Segment, Rotate, Angle, and Intersect to create objects like A_1, B_1, a, A', A, b, B', B, c, C, d, X, etc. It is suitable for middle school and above students studying geometric transformations and properties of similar figures, ideal for classroom instruction or self-exploration.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → a
  2. Rotate(A_1, -36*°, B_1) → A'
  3. Angle(A', B_1, A_1) → A
  4. Segment(B_1, A') → b
  5. Rotate(B_1, 30*°, A_1) → B'
  6. Angle(B_1, A_1, B') → B
  7. Segment(A_1, B') → c
  8. Intersect(b, c) → C
  9. Segment(A_1, C) → d
  10. Angle(A', C, A_1) → X