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The Properties of rigid transformations exercise appeared under the 8th grade (U.S.) Math Mission and the Geometry Math Mission. This exercise uses rigid transformations to explore invariant properties within Euclidean geometry.

Types of Problems

There are three types of problems in this exercise:

  1. Perform the reflection and answer the questions: This problem asks the user to perform the specified rigid transformation. After doing this, they are asked to answer several questions based on the image after the transformation is performed.
    Port1

    Perform the reflection and answer the questions

  2. Perform the translation and answer the questions: This problem asks the user to perform the specified rigid transformation. After doing this, they are asked to answer several questions based on the image after the transformation is performed.
    Port2

    Perform the translation and answer the questions

  3. Perform the rotation and answer the questions: This problem asks users to perform the specified rigid transformation. After doing this, they are asked to answer several questions based on the image after the transformation is performed.
    Port3

    Perform the rotation and answer the questions

Strategies

Knowledge of the basic rigid transformations (including reflection) are all that is needed to do this exercise accurately and efficiently. The answers to the questions are often the same regardless of the transformation performed.

  1. The manipulative is easy to use. It will label/describe the transformation being performed so just make sure it matches the request.
  2. Lines, segments, and angles are sent to lines, congruent segments and congruent angles by rigid transformations.
  3. Lines have no endpoints and extend forever in both directions, segments have two endpoints.
  4. Parallelism is also invariant under rigid transformations.

Real-life applications

  1. Knowledge of the Rigid transformations can be used to understand the Erlanger Programm, a method for developing and classifying non-Euclidean geometries (such as space might be).

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