The Exploring rigid transformations and congruence exercise appears under the 8th grade (U.S.) Math Mission and the High school geometry Math Mission. This exercise practices using a composition of various isometries to map one polygon into another.

Types of Problems

There is one type of problem in this exercise:

  1. Transform polygon into the other and answer question: This problem provides a grid with two polygons that should appear to be congruent. The user is asked to define a sequence of rigid maps that can transform one polygon into the other. After completed, the student is asked to determine if the polygons are congruent or not.

    Transform the polygon into the other and answer question


The manipulative makes accuracy badges and speed badges straightforward on this exercise. Efficiency will come from with experience and practice with earlier transformation exercises.

  1. A translation is a slide, a rotation is a turn and a reflection is a flip.
  2. It is recommended first to reflect (over any line) if orientation is reversed.
  3. Once orientation is correct, it is recommended to move any vertex onto a corresponding vertex via a translation.
  4. One a vertex is aligned, a rotation about that vertex will move the polygon as close as it possibly can get to the other polygon.
  5. Two shapes are congruent if and only if they can be lined up perfectly.
  6. If the shapes are not similar, it is not necessary to perform any transformations, one may just click "not similar" and submit.

Real-life applications

  1. Pattern recognition is useful for developing Frieze patterns as well as on certain intelligence tests (such as IQ tests).
  2. An ability to visualize how shapes move can assist with many activities from completing jigsaw puzzles to packing boxes more efficiently.

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