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Definition and Construction of Congruent Circles

Definition and Construction of Congruent Circles
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2016-07-01 07:03
CircleTransformationGeometric Construction
In collections Circles (Theorems) Circle Terms
This example demonstrates the definition and properties of congruent circles. Key math concepts include congruent figures, circle definitions, and geometric transformations. Construction highlights involve using GeoGebra commands like Circle, Point, Segment, Line, Dilate, Vector, Translate, Angle, and Rotate. Suitable for high school mathematics instruction on understanding congruent circle determination and construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → G
  3. Segment(A, B) → f
  4. Circle(C, f) → d
  5. Point(d) → D
  6. Line(C, D) → h
  7. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], G) → A'
  8. Segment(A, A') → i
  9. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], D) → C'
  10. Segment(C, C') → j
  11. Dilate(G, If[1 < a ≤ 2, 2 - a, 0], D) → G'
  12. Vector(G, G') → u
  13. Translate(A, u) → A'_1
  14. Translate(A', u) → A''
  15. Segment(A'_1, A'') → i'
  16. Line(D, i) → g
  17. Point(g) → E
  18. Angle(E, D, C) → α
  19. Rotate(A'_1, If[2 < a ≤ 3, ((a - 2) * α), α], D) → F
  20. Rotate(A'', If[2 < a ≤ 3, ((a - 2) * α), α], D) → A'''
  21. Segment(F, A''') → i''