Chapter 3
Rigid Transformations and Symmetry
Two paper cutouts look alike, but they lie in different positions on a desk. How could you check whether they match exactly? Comparing a few corners may miss something. Rigid transformations invite us to follow where every point of a figure goes and investigate what stays unchanged. Describing these motions gives us a new way to ask whether one whole figure can match another. What evidence would convince you that the match is exact?
What You'll Explore
5 lessons.
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How can you describe a slide precisely enough for someone else to move every point to the intended place? Follow points on and off a grid as you compare their journeys and investigate what happens to the figure's measurements.
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Which details decide where a point appears in a mirror image? Starting with a paper fold, you will investigate the connection between a figure, its image, and the mirror line, including what happens when a point lies on the fold.
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What information would someone need to reproduce a turn of a figure exactly? You will explore point paths around a center and examine clues left by a figure and its image, asking how those clues can help describe the turn.
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Does changing the order of two motions change where a figure lands? Compare different sequences, then investigate how describing a sequence could help you decide whether two whole figures are congruent.
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Can a figure move and still match its original position exactly? Test proposed flips and turns on whole figures, including some that look promising at first, to investigate the different kinds of symmetry these motions might reveal.