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Lesson 5 of 9

Matching partway through a turn

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6 min

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Spin a square card on a table with one finger. It looks the same four times in one full spin. A full turn is 360°. A quarter turn is 90°.

Start. One corner is marked.
Step 1 of 4
  1. Start. One corner is marked.
  2. Turn it 90°. The marked corner moves. The square looks the same.
  3. Turn it 180°.
  4. Turn it 270°. A fourth turn returns it to Start.

Turning

Turn a square 90° around its middle point. The square lands back on itself. It does so at 180°, 270° and 360° too. Matching itself after a turn is rotational symmetry. The order is how often a shape matches in one full circle. A square has order 4.

No fold line needed

Take a leaning four-sided shape. Its opposite sides are equal. It has no fold line. Yet turning it 180° lands it back on itself. It matches at 180° and 360°. So its order is 2. Folding and turning are separate tests. Every shape matches itself after a full turn. So order 1 means no turning symmetry.

Slide the turn in the lab. Watch for the matches. Then tap Next shape.

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Try the lab to finish this lesson.