Grade by Grade
E. Spatial Sense · Shapes, Maps and Measurement

Lines of Symmetry

E1.1About 30 minutes
Learning goals
  • I can find a line of symmetry by folding or by using a mirror.
  • I can count how many lines of symmetry a shape has (0, 1, 2 or more).
  • I can complete a picture so that it is symmetrical.
  • I can sort shapes by the number of lines of symmetry.

Words to know

symmetry
When one half of a shape is a mirror image of the other half.
line of symmetry
A line that cuts a shape into two matching halves. If you fold on the line, the halves fit exactly on top of each other.
symmetrical
Having at least one line of symmetry.
mirror image
A copy that is flipped, like your reflection in a mirror.

Remember from Grade 1

In Grade 1 you folded shapes to find matching halves. A butterfly, a maple leaf and a heart all have two halves that match.

This year you will find out that some shapes have more than one way to fold into matching halves!

A single red maple leaf lying flat on a light wooden table.
Imagine a line running down the middle of this maple leaf, along its stem. The left and right halves are very close to mirror images, so the leaf has a line of symmetry. AI-generated image

What is a line of symmetry?

A line of symmetry cuts a shape into two halves that are mirror images.

Here is how to test a line:

  1. Fold the shape on the line.
  2. Look at the two halves. Do they fit exactly on top of each other, with nothing sticking out?
  3. If yes, it is a line of symmetry!

You can also stand a small mirror on the line. If the reflection makes the whole shape look complete, it is a line of symmetry.

1 line2 lines4 lines
The dashed lines are lines of symmetry. This triangle has 1, the rectangle has 2, and the square has 4.
Worked example

Example 1: Lines of symmetry in a rectangle

Cut out a paper rectangle (not a square). How many lines of symmetry does it have?

  1. Fold it top to bottom so the long sides meet. The halves match. That is 1 line.
  2. Unfold. Fold it side to side so the short sides meet. The halves match. That is 2 lines.
  3. Unfold. Try folding from corner to corner (the diagonal). The flaps stick out and do not match. Not a line of symmetry.

A rectangle has 2 lines of symmetry.

Fold on the diagonal?The flaps do not match.Not a line of symmetry!
Folding a rectangle on the diagonal does not make matching halves.

Squares are special

A square has 4 lines of symmetry: up and down, side to side, and both diagonals (corner to corner). That is 2 more than a rectangle, because all its sides are the same length.

3 lines6 linestoo many to count!
A triangle with 3 equal sides has 3 lines. A hexagon with all sides equal has 6. A circle has so many we can't count them all!

Some shapes have no lines of symmetry

Not every shape is symmetrical. A pushed-over parallelogram has 0 lines of symmetry. A triangle with three different side lengths has 0 lines too. However you fold them, the halves do not match.

parallelogram: 0 linesno equal sides: 0 lines
These shapes have no lines of symmetry.
Worked example

Example 2: Complete the picture

The dashed line is a line of symmetry. The left side of the picture is coloured. Colour the right side so the picture is symmetrical.

  1. Look at one row at a time.
  2. Find each coloured square on the left. Count how many squares it is from the line.
  3. Colour the square that is the same number of squares away on the right side.
  4. Check: if you fold on the line, every coloured square lands on another coloured square.

The finished picture looks like a tree. Both sides match.

Colour the right side to match.
Before: only the left side is coloured.
Each square is the same distance from the line.
After: the right side is a mirror image of the left side.
ShapeLines of symmetry
triangle with no equal sides0
pushed-over parallelogram0
triangle with 2 equal sides1
rectangle (not a square)2
triangle with 3 equal sides3
square4
hexagon with all sides and angles equal6
circletoo many to count
Sorting shapes by their number of lines of symmetry
Just for fun

Some words have a line of symmetry right down the middle! Print WOW, MOM or TOOT in capital letters, then fold the paper or hold it up to a mirror.

Hands-on activity

Fold, cut and check

You need: paper, scissors (with a grown-up's help), a small mirror if you have one.

  1. Cut out a square, a rectangle and a triangle from paper.
  2. Fold each shape in every way you can think of. Each time the halves match, draw along the fold with a pencil.
  3. Count the pencil lines on each shape. Did you find 4, 2 and 0, 1 or 3?
  4. Fold a piece of paper in half. Cut out half a heart, half a person or half a maple leaf along the fold. Open it up. The fold is a line of symmetry!
  5. Look at the letters of your name. Which letters have a line of symmetry? Test them with a mirror.

Math talk: "How do you know that fold is a line of symmetry?"

Your turn

1

How many lines of symmetry does a square have?

2

How many lines of symmetry does a rectangle that is not a square have?

3

You fold a shape and the two halves do not match. Is the fold a line of symmetry?

4

Does the capital letter A have a line of symmetry? Where?

5

Does the capital letter H have a line of symmetry? How many?

6

Name something in nature that is symmetrical.

More practice: warm-up

1

What do you call a line that cuts a shape into two matching halves?

2

How many lines of symmetry does a circle have?

3

Does the letter T have a line of symmetry?

4

What tool can you use instead of folding to check for symmetry?

5

True or false: every shape has at least one line of symmetry.

More practice: on your own

1

Which has more lines of symmetry, a square or a rectangle (not a square)? How many more?

2

Does the letter F have a line of symmetry? Explain.

3

Sort these letters into "has a line of symmetry" and "has no line of symmetry": M, R, O, L, W.

4

A triangle has 2 sides the same length. How many lines of symmetry does it have, and where is the line?

5

Sam says the line from one corner to the opposite corner is a line of symmetry for every rectangle. Is Sam right?

Challenge

1

How many lines of symmetry does a stop sign shape (an octagon with all sides equal) have? Hint: a hexagon with all sides equal has 6.

2

Draw a shape that has exactly 1 line of symmetry. Describe it.

3

The word MOM is written in capitals. Does the whole word have a line of symmetry? Where?

Check your understanding

Quiz

1.

What happens when you fold a shape on a line of symmetry?

2.

How many lines of symmetry does a square have?

3.

How many lines of symmetry does a rectangle (not a square) have?

4.

Which letter has no line of symmetry?

5.

Which shape has 0 lines of symmetry?

6.

A triangle has 3 equal sides. How many lines of symmetry does it have?

For parents and teachers

Big idea: A line of symmetry splits a shape into two mirror-image halves. In Grade 2, children count lines of symmetry and use this as one more way to sort shapes.

Common difficulties:

  • Thinking a rectangle's diagonal is a line of symmetry. Let your child fold a paper rectangle corner to corner to see the flaps that stick out. Seeing it is more convincing than being told.
  • Copying instead of flipping when completing a picture. Remind them to count squares away from the line on both sides.
  • Letters: answers depend a little on the font. Use plain capital letters, like on a keyboard.

How to help: Fold paper shapes, cut paper snowflakes and look for symmetry in nature (leaves, insects, flowers). A small hand mirror is a great tool for checking.