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Bottema's Theorem

Bottema's Theorem
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2021-12-18 22:48
TriangleComplex NumberGeometric Construction
This GeoGebra applet demonstrates Bottema's theorem, which involves special points in triangles. By constructing an isosceles right triangle, the trajectory of the third vertex is found to be a circle. The construction uses commands such as Spline, Point, Mirror, Polygon, Midpoint, and Segment, suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Spline(l1, 3) → a
  2. Point(xAxis) → A
  3. Mirror(A, yAxis) → A'
  4. Polygon(A', B, 4) → poly1, f, g, h, i, C, D
  5. Polygon(B, A, 4) → poly2, j, k, l, m, E, F
  6. Midpoint(D, E) → G
  7. Segment(D, G) → n
  8. Segment(G, E) → p
  9. Segment(A', A) → q
  10. Segment(D, G) → r
  11. Segment(G, E) → s

AI Drawing Prompt Reference

Draw an isosceles right triangle and find the trajectory of its third vertex, which should form a circle. Start by drawing a line segment, then take points on it. Mirror points to construct the triangle, find midpoints of two triangles, connect midpoints to vertices, and finally connect the vertices in order to form the trajectory circle.
The prompt above was compiled from the original drawing commands and is for reference only.