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Perpendicular Bisector Theorem (Part 2)

Perpendicular Bisector Theorem (Part 2)
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2016-06-20 20:14
TriangleCircleGeometric Construction
This example demonstrates a more scaffolded version of the Perpendicular Bisector Theorem. It involves the properties of circles and geometric construction. Using GeoGebra commands such as Segment, LineBisector, Circle, Intersect, etc., the core concept of the theorem is clearly illustrated. Suitable for students at the junior high school level and above to learn about geometric construction and properties of circles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. LineBisector(f) → p
  3. Point(p) → C
  4. Midpoint(f) → C_1
  5. Circle(C_1, (0.1 * f)) → c
  6. Intersect(c, f, 2) → D
  7. Intersect(c, p, 2) → E
  8. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C_1) → A'
  9. Segment(A, A') → h
  10. Dilate(C_1, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  11. Segment(C_1, C') → i
  12. Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * π), (-π)], C_1) → A'_1
  13. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], C_1) → A''
  14. Segment(A'_1, A'') → h'
  15. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], C) → A'_2
  16. Segment(A, A'_2) → g
  17. Dilate(B, If[1 < e ≤ 2, 2 - e, 0], C) → B'
  18. Segment(B, B') → j
  19. Angle(A, C, B) → α
  20. Rotate(A, If[2 < e ≤ 3, ((e - 2) * α), α], C) → A'_3
  21. Rotate(A'_2, If[2 < e ≤ 3, ((e - 2) * α), α], C) → G
  22. Segment(A'_3, G) → g'
  23. Angle(C, C_1, A) → β