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Lines of symmetry of a square

Step by step, with the reason for every step · Symmetry · Geometry

Step by step

The question

Question: how many lines of symmetry does a square have?

1 Try the folds

Imagine folding the shape along a line.

If the two halves match exactly, it is a line of symmetry.

Fold through the middles of two opposite sides.

The halves match: line 1.

Fold through two opposite corners.

The halves match: line 2.

Fold through the middles of two opposite sides.

The halves match: line 3.

Fold through two opposite corners.

The halves match: line 4.

2 Count the lines

We found 4.

So a square has 4 lines of symmetry.

lines of symmetry = 4

Careful!

Do not stop at the folds through the corners.

The folds through the middles of the sides count too: 4, not 2.

Careful: not 2 ✗

3 Check

Let's check: a regular shape has as many lines of symmetry as sides.

4 sides, 4 lines.

Right!

4 sides → 4 lines

Let's look back.

First: try the folds.

Then: count the lines.

Last: check.

Answer
lines of symmetry = 4

Your turn

Try this one yourself, then check:

Regular pentagon: how many lines of symmetry?
Show the answer
lines of symmetry = 5

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