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Symmetry

Not every middle line

A rectangle has a line drawn corner to corner. The line makes two equal halves. Is it a fold line, a line of symmetry?

A rectangle, 8 cm by 5 cm. A line runs corner to corner.
Step 1 of 3
  1. A rectangle, 8 cm by 5 cm. A line runs corner to corner.
  2. Fold along that line. The copy leans over.
  3. Two corners land off the shape, 2.2 cm past the edge.

The test

No. Equal halves do not always fit when folded.

Fold the shape along the line. Every part must land on the shape. Then the line is a line of symmetry. If one part lands off the shape, the line is not one.

Here, 4 of 40 tested points land back on the rectangle. The other 36 land off it. The worst miss is 2.2 cm past the edge.

In the lab, look at each dashed line. Choose Yes or No. Then watch the real fold.

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This track

  1. 0 Start here
  2. 1 Fold it, and it matches
  3. 2 Not every middle line
  4. 3 How many fold lines?
  5. 4 Symmetry around us
  6. 5 Matching partway through a turn
  7. 6 Half a picture decides the rest
  8. 7 The big picture
  9. 8 Track quiz

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