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Transformations

Dive into the world of congruency and transformations in geometry. This guide covers the definitions and significance of congruency, exploring when two shapes or figures are considered congruent. Learn about various types of isometries, including reflection, translation, rotation, and glide reflection, that preserve distances between points. Engage with strategic activities to visualize congruency and develop insights into transformations. Conjecture the outcomes of multiple transformations and solidify your understanding through homework sections.

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Transformations

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  1. Transformations Math AllianceJanuary 11, 2011

  2. What is Congruency? • Define it: • Alone • As a group • Ideas?

  3. When are 2 Shapes or Figures Congruent? • We’ve put congruency into words; now how could you show congruency? • Develop a strategy with your table. • Ideas?

  4. Transformation • Definition: • Movement of points in the plane. • Notation: • The image of point P under a transformation will be written P’

  5. Isometry • Definition: • Movements of points in the plane that preserve the distance between points: the distance between P and Q is equal to the distance between P’ and Q’. • What types of isometry do you know?

  6. Isometry • Definition: • Movements of points in the plane that preserve the distance between points: the distance between P and Q is equal to the distance between P’ and Q’. • Types: • Reflection • Translation • Rotation • Glide reflection

  7. B C A = A’ D B’ D’ C’ Name the Transformation: Reflection

  8. D’ C = C’ B A’ A D B’ Name the Transformation: Rotation

  9. C’ B’ C B A’ D’ A D Name the Transformation: Translation

  10. C B A D A’ D’ B’ C’ Name the Transformation: Glide Reflection

  11. C B l A m n Make a conjecture: What will happen if you transform ABC over n and then over m?

  12. C B l A m n Make a conjecture: What will happen if you transform ABC over n and then over l?

  13. C B l A n Make a conjecture: What will happen if you reflect ABC over n and then over l?

  14. Homework: • Read Section 11.1 • Section 11.1 #’s: 1-10, 23, 25, 30, 38a, 38h, 40b, and 46

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