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Messing with Lisa: Interactive Intro to Transformational Geometry

Messing with Lisa: Interactive Intro to Transformational Geometry
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2016-07-01 20:49
AngleVectorTransformationGeometric ConstructionSlider Animation
In collections Congruence (CO) Cluster Congruence (Vol 1) Geometry Review Congruence (Vol 1) Over 80 Resources Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 Transformations! (Geometry) Transformations/Symmetry Prove Congruence through Transformations
① This example demonstrates how a playful graphic (a stylized portrait named 'Lisa') can be transformed through translation, rotation, reflection, and dilation, showing changes in position, orientation, and size. ② Core mathematical concepts include geometric transformations (translation, rotation, reflection, dilation), vectors, angles, area, and even polynomial functions and slope as extensions. ③ Construction highlights: using GeoGebra commands like Vector, Translate, Rotate, CircleArc, Circle, Line, Mirror, Dilate, and Textfield, the applet creates multiple transformed copies (e.g., pic1', B', C') and allows interactive control via sliders or buttons. ④ This is ideal for middle school to high school students learning transformational geometry, and for teachers to demonstrate transformation properties and compositions in a dynamic, visual way.

GeoGebra Commands & Parameters

  1. Vector(D, E) → u
  2. Translate(pic1, u) → pic1'
  3. Translate(B, u) → B'
  4. Translate(C, u) → C'
  5. Vector(B, B') → v
  6. Rotate(C, δ, A) → C'_1
  7. CircleArc(A, C'_1, C) → c
  8. CircleArc(A, C, C'_1) → d
  9. Circle(A, C) → e
  10. Line(F, G) → f
  11. Mirror(pic1, f) → pic1'_2
  12. Mirror(B, f) → B'_2
  13. Mirror(C, f) → C'_2
  14. Dilate(pic1, k, A) → pic1'_3
  15. Dilate(B, k, A) → B'_3
  16. Dilate(C, k, A) → C'_3
  17. Rotate(B, δ, A) → B'_1
  18. Rotate(pic1, δ, A) → pic1'_1
  19. Circle(A, C) → p
  20. CircleArc(A, C'_1, C) → r
  21. Textfield(δ) → InputBox1
  22. Textfield(k) → InputBox2