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Translations

This text explores the concept of translations in geometry, highlighting how shapes like points, triangles, and line segments are moved uniformly in the same direction and distance. We demonstrate through mapping that the images of triangles under translation maintain congruence, while line segments remain equal and parallel. Various examples illustrate transformations between different shapes, allowing for a clear understanding of the geometric implications of translations. This study serves as a fundamental basis in geometric transformations, essential for advanced mathematics and physics.

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Translations

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Presentation Transcript

  1. z q c x p y d cd Translations

  2. a b c d ab cd Translation A translation moves every point the same distance in the same direction

  3. p b q c d a xy pq y x

  4. b d a c xy y The image of a line segment under a translation is an equal and parallel line segment x

  5. p q pq The image of a triangle under a translation is a congruent triangle

  6. maps xyz  ypq xy xy xy maps x  y y  p z  q z q x p y

  7. maps abcd  befc ab ab ab a b e c f d a  b b  e c  f d  c

  8. maps abcd  dcgh ac ac ac a b a  d b  c d c c  g d  h g h

  9. a a b b c c d d e e f f m n maps [dm]  [en] ab ab ab ab m  n m n d  e m  n

  10. a b c d e f a b c m n maps adm  ben maps abed  bcfe d e f ab ab ab ab ab a  b d  e m  n m n a  b b  c e  f d  e

  11. a a b b c c d d e e f f m n maps [dm]  [en] maps  bde   cef ab ab ab ab ab b  c d  e m n e f a  b e  f

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