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Doubling and Halving an Isosceles Right Triangle

Doubling and Halving an Isosceles Right Triangle
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2015-11-15 00:47
TriangleSequenceGeometric Construction
In collections About Exponents
This example demonstrates powers of 2 by doubling and halving an isosceles right triangle. It involves core math concepts like isosceles right triangles, midpoints, lines, orthogonal lines, intersections, sequences, and rotations. The construction uses GeoGebra commands such as Polygon, Midpoint, Line, OrthogonalLine, Intersect, Sequence, and Rotate. Suitable for middle school and above students exploring geometric transformations and algebraic relationships.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → tri, c, a, b
  2. Midpoint(C, B) → D
  3. Line(D, A) → d
  4. OrthogonalLine(C, d) → e
  5. Intersect(d, e) → E
  6. Sequence(Rotate[Polygon[Dilate[A, r^(k), E], Dilate[B, r^(k), E], Dilate[C, r^(k), E]], (t * k), E], k, 0, abs(n)) → list1
  7. Sequence(Rotate[Polygon[Dilate[A, r^((-k)), E], Dilate[B, r^((-k)), E], Dilate[C, r^((-k)), E]], ((-t) * k), E], k, 0, abs(n)) → list2
  8. Rotate(Polygon[Dilate[A, r^(n), E], Dilate[B, r^(n), E], Dilate[C, r^(n), E]], (t * n), E) → poly1