Line symmetry

Fold it and it lines up

Cut a heart from paper: fold the paper in half, cut half and unfold. You get a heart whose left half is an exact mirror of the right.

Such a shape is called line-symmetric. The line along which you folded the paper — that fold in the middle — is the line of symmetry: a mirror laid into the picture.

The symmetry test is exactly folding: when you fold the shape along the line and both halves line up exactly, it is symmetric.

Symmetry is everywhere: a butterfly (the line goes through the body), a human face (roughly), the letters A, O, T, M, a heart, a snowflake. A square is a symmetry champion — it has four lines at once.

Today you will look for symmetry, test it by folding and above all finish drawing: you get half a picture with a line and you finish the mirror other half. Squared paper will be your mirror.

Adam is making a carnival mask. He draws it freehand and the result is crooked — one eye higher, a corner of the mouth down. His sister advises a trick: “Fold a card in half, draw only half the mask from the fold and cut it folded.” Adam unfolds the paper and stares: the mask is perfectly symmetric, both eyes equally high. The fold in the middle is the line of symmetry and the scissors cut both halves at once — the right is a mirror of the left, however he tried.

A folding test and finishing the other half

Symmetry test (a paper shape):

1. Guess where the line could go.
2. Fold the shape along the guessed line.
3. Do both halves line up exactly? The line is true and the shape is symmetric. Does something stick out? Try another line — or the shape is not symmetric.

Some shapes have more lines: a rectangle two (horizontal and vertical), a square four (plus both diagonals), a circle infinitely many. And say the letter F has none.

Finishing the mirror half on squared paper:

1. Find a clear point on the half picture (a corner of a line).
2. Count the squares from the point to the line: say 3.
3. Mark the same number of squares on the other side of the line — the same distance, straight across the line — and make a dot.
4. Repeat for all the corners of the picture.
5. 참여 the dots with the same lines as in the original.

An important rule: a mirror flips sides. What is in the original left of the line will be in the image on the right. What touches the line stays in place — a point on the line is its own mirror.

How many lines a square has

I cut out a square and look for lines by folding.

Try 1: I fold in half horizontally — it lines up. Line 1.

Try 2: vertically — it lines up. Line 2.

Try 3: along a diagonal (corner to corner) — it lines up! Line 3.

Try 4: the other diagonal — it lines up. Line 4.

A square has 4 lines of symmetry. A rectangle (not a square one) only 2 — a diagonal fold does not line up with it, check with paper.

Symmetric letters

I look at capital printed letters: A, B, C, F.

A: a vertical line through the middle — left and right half line up. Symmetric.

B: a vertical line does not work (the bumps are only on the right), but a horizontal one through the middle does. Symmetric.

C: a horizontal line through the middle. Symmetric.

F: vertical does not line up, horizontal neither (the bars are only at the top). Not symmetric.

A nice task for the curious: H and O have two lines (H) — and how many does O have?

Finishing a butterfly

On squared paper there is a left butterfly wing and a vertical line (the body). I finish the right one.

Step 1: the tip of the wing is 4 squares left of the line, 2 up. I make a dot 4 squares right of the line, 2 up.

Step 2: the bottom corner of the wing: 3 left, 1 down → a dot 3 right, 1 down.

Step 3: that way I transfer all the corners and join them.

Check: I fold the paper along the line against a window — the wings line up. The butterfly flies.

Play it

Before you go to the sheet, try it with your eyes. This is not a test — it is a game. Tap until you see it.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 시작 with ten. When it goes well, add more.

Does a letter have a line? Fold it in your head along the line.

Practise the questions

On paper

Scissors, squared paper and a small mirror from a pencil case if you like.

1. Fold paper, from the fold draw half a heart or half a mask, cut it folded and unfold. Mark the line in pencil.

2. Write the capital printed letters of your name and for each decide: does it have a line? Vertical, horizontal, none?

3. On squared paper draw a vertical line and left of it a simple shape of straight lines (an arrow, a little tree). Finish the mirror half by counting squares.

4. Cut out a rectangle and a square. By folding find all the lines and count them (2 and 4). The folds after folding will mark them for you.

Now you 💪

1. You know the symmetry test: fold along the line, the halves must line up.
2. By folding you find all 4 lines of a square.
3. You finish the mirror half of a picture by counting squares from the line.

What to take from this lesson

• A line-symmetric shape has two halves that line up after folding along the line.
• A line of symmetry is a mirror laid into the picture — on a cut-out it is the fold.
• A shape can have more lines: a rectangle 2, a square 4, a circle infinitely many.
• Finishing: each point the same distance from the line, only on the other side.
• A mirror flips sides — left becomes right, points on the line stay.

© 2026 Ing. Martin Polak / AlgoRhino · 콘텐츠 이용 약관