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Composing Transformations: Example 20

Composing Transformations: Example 20
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2018-05-28 13:09
Coordinate GeometryTransformationGeometric Construction
In collections Geometry Review Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 Beginner Tutorials
This interactive investigation demonstrates the composition of two line reflections. Key mathematical concepts include reflection transformations and transformation composition. Using GeoGebra commands such as Rotate, Mirror, and Intersect, the composition of two line reflections can be constructed. Suitable for middle school and above students or teachers for teaching geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(B, (a * π / 180), A) → B'
  2. Line(A, B') → f
  3. Rotate(B', (b * π / 180), A) → B''
  4. Line(A, B'') → g
  5. Rotate(pic1, β, A) → pic1'_1
  6. Rotate(C, β, A) → C'_1
  7. Rotate(D, β, A) → D'_1
  8. Mirror(B', A) → B''_1
  9. Mirror(B'', A) → B'''
  10. Circle(A, (3 * Distance[A, B])) → c
  11. Intersect(c, f, 1) → E
  12. Intersect(c, g, 1) → F
  13. Angle(E, A, F) → α
  14. Segment(C, A) → h
  15. Segment(A, C'_1) → i
  16. Angle(C, A, C'_1) → γ