GEOM.MATH.3.B

Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane; Page 10 October 2015 Update.

Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
imagepre-imagetwo-dimensional figurecompositionrigid transformationsnon-rigid transformationsdilationscenterplane
Skills
  • determine (the image or pre-image of a two-dimensional figure under a composition of transformations) #dok2
  • identify (compositions of rigid and non-rigid transformations) #dok2
  • apply (dilations with the center at any point in the plane) #dok3
  • differentiate (between rigid and non-rigid transformations in compositions) #dok2
Learning Targets
  • I can determine the image or pre-image of a two-dimensional figure under a composition of rigid transformations. #dok2
  • I can determine the image or pre-image of a two-dimensional figure under a composition of non-rigid transformations. #dok2
  • I can differentiate between rigid and non-rigid transformations when analyzing figures. #dok2
  • I can apply dilations to figures when the center is any point in the plane. #dok3
  • I can analyze and predict the outcome of a composition of different types of transformations. #dok3
Big Ideas
  • Compositions of transformations change figures in predictable ways, whether using rigid motions or dilations.
  • Understanding the effect and sequence of transformations is critical to analyzing geometric relationships and similarity.
Essential Questions
  • How can the outcome of a composition of transformations be determined for any figure?
  • In what ways do rigid and non-rigid transformations differ when applied in sequences?
  • What is the effect of changing the center of dilation on the image of a figure?
  • How can you distinguish between the image and pre-image in a series of transformations?
  • Why is it important to understand compositions of transformations in geometry?