Year 4: Lines of symmetry
Part of the Year 4 shapes, angles and symmetry chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Lines of symmetry
A shape has a line of symmetry if you can fold it along a line so that the two halves fit exactly on top of each other. The line is also called a mirror line, because one half is the mirror image of the other half. Some shapes have one line, some have many, and some have none.
Regular polygons have as many lines of symmetry as they have sides: a regular pentagon has 5 and a regular hexagon has 6.
Different orientations. A shape can be turned round. A turned shape has the same number of lines of symmetry, but the lines point in different directions. A line of symmetry can be vertical (up and down), horizontal (across) or sloping.
Letters and patterns. Some capital letters have lines of symmetry. The letter H has two: one up and down and one across. The letter A has one. The letter N has none. Patterns made of coloured squares can also have lines of symmetry, even diagonal ones.
Key ideas
- A line of symmetry (mirror line) is a fold line that makes the two halves match exactly.
- A shape can have 0, 1, 2 or more lines of symmetry. A regular polygon has as many lines as sides.
- Turning a shape round does not change its number of lines of symmetry.
- A rectangle has 2 lines of symmetry (not the diagonals). A parallelogram has none.
- Check lines by folding, or by imagining a mirror. Letters and patterns can have lines too.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The rectangle has 2 lines of symmetry.
- Check the diagonals. A diagonal is a line from corner to corner. Fold along it: the corners do not fit on top of each other.The diagonals are not lines of symmetry.
- Write the answer. 2
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The isosceles triangle has 1 line of symmetry.
- Count the lines. The number of lines of symmetry is 1.
- Write the answer. 1
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The regular pentagon has 5 lines of symmetry.
- Count the lines. The number of lines of symmetry is 5.
- Write the answer. 5
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine folding the shape along the dashed line. If the two halves fit exactly on top of each other, it is a line of symmetry. The orange outline shows where the other half lands after the fold.
- Look at the dashed line. It is the fold line.
- Fold along the line. The orange outline is the reflection: where each corner lands after the fold.
- Compare the two halves. Do the orange lines lie exactly on the shape’s edges?No. The orange outline sticks out of the shape, so the halves do not fit.
- Answer. No, it is not a line of symmetry.
Check. A rectangle does not have a line of symmetry here. ✓
Watch out. A line that cuts a shape into two equal halves is not always a line of symmetry. The two halves must be mirror images.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror standing up the middle of the letter (a vertical line) and another lying across the middle (a horizontal line). If one half is the mirror image of the other, it is a line of symmetry.
- Look at the letter E. The red dashed lines are the lines of symmetry.
- Test the up-and-down (vertical) line. Do the left and right halves match?No.
- Test the across (horizontal) line. Do the top and bottom halves match?Yes.
- Count. The letter E has 1 line of symmetry.
Check. Fold a copy of the letter along each line to check. ✓
Watch out. Look at the letter as a block shape.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror along each possible line: up and down, across, and the two corner-to-corner lines. Check each one: does the shaded pattern match on both sides?
- Test the vertical line (up and down). Compare the left and right sides.Does not match.
- Test the horizontal line (across). Compare the top and bottom.Does not match.
- Test the two diagonal lines. Compare the two sides of each corner-to-corner line.The \ diagonal matches. The / diagonal does not match.
- Count the lines. The red lines are the lines of symmetry.The pattern has 1 line of symmetry.
Check. Fold along each red line: the shaded squares land on shaded squares. ✓
Watch out. Do not forget the diagonal lines.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.There is no fold line that makes the two halves match.
- Look for every line. Try lines through the corners and through the middles of the sides.The parallelogram has no lines of symmetry.
- Try some fold lines. Fold along a diagonal or along a line through the middle. The halves do not match.No fold line works.
- Write the answer. 0
Check. Try folding in several ways: the halves never fit. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Watch out
The diagonals of a rectangle are not lines of symmetry. A rectangle has only 2 lines: through the middles of opposite sides. If you fold it along a diagonal, the corners do not land on each other. Also remember: a line that cuts a shape into two equal pieces is not always a line of symmetry. The two halves must be mirror images.Exercise 9G Lines of symmetry
Non-calculatorKey words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine folding the shape along the dashed line. If the two halves fit exactly on top of each other, it is a line of symmetry. The orange outline shows where the other half lands after the fold.
- Look at the dashed line. It is the fold line.
- Fold along the line. The orange outline is the reflection: where each corner lands after the fold.
- Compare the two halves. Do the orange lines lie exactly on the shape’s edges?Yes, they match exactly.
- Answer. Yes, it is a line of symmetry.
Check. A rectangle has a line of symmetry here. ✓
Watch out. A line that cuts a shape into two equal halves is not always a line of symmetry. The two halves must be mirror images.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine folding the shape along the dashed line. If the two halves fit exactly on top of each other, it is a line of symmetry. The orange outline shows where the other half lands after the fold.
- Look at the dashed line. It is the fold line.
- Fold along the line. The orange outline is the reflection: where each corner lands after the fold.
- Compare the two halves. Do the orange lines lie exactly on the shape’s edges?No. The orange outline sticks out of the shape, so the halves do not fit.
- Answer. No, it is not a line of symmetry.
Check. A rectangle does not have a line of symmetry here. ✓
Watch out. A line that cuts a shape into two equal halves is not always a line of symmetry. The two halves must be mirror images.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine folding the shape along the dashed line. If the two halves fit exactly on top of each other, it is a line of symmetry. The orange outline shows where the other half lands after the fold.
- Look at the dashed line. It is the fold line.
- Fold along the line. The orange outline is the reflection: where each corner lands after the fold.
- Compare the two halves. Do the orange lines lie exactly on the shape’s edges?Yes, they match exactly.
- Answer. Yes, it is a line of symmetry.
Check. A kite has a line of symmetry here. ✓
Watch out. A line that cuts a shape into two equal halves is not always a line of symmetry. The two halves must be mirror images.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine folding the shape along the dashed line. If the two halves fit exactly on top of each other, it is a line of symmetry. The orange outline shows where the other half lands after the fold.
- Look at the dashed line. It is the fold line.
- Fold along the line. The orange outline is the reflection: where each corner lands after the fold.
- Compare the two halves. Do the orange lines lie exactly on the shape’s edges?No. The orange outline sticks out of the shape, so the halves do not fit.
- Answer. No, it is not a line of symmetry.
Check. A parallelogram does not have a line of symmetry here. ✓
Watch out. A line that cuts a shape into two equal halves is not always a line of symmetry. The two halves must be mirror images.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The square has 4 lines of symmetry.
- Count the lines. The number of lines of symmetry is 4.
- Write the answer. 4
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The rectangle has 2 lines of symmetry.
- Check the diagonals. A diagonal is a line from corner to corner. Fold along it: the corners do not fit on top of each other.The diagonals are not lines of symmetry.
- Write the answer. 2
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The equilateral triangle has 3 lines of symmetry.
- Count the lines. The number of lines of symmetry is 3.
- Write the answer. 3
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The kite has 1 line of symmetry.
- Count the lines. The number of lines of symmetry is 1.
- Write the answer. 1
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.There is no fold line that makes the two halves match.
- Look for every line. Try lines through the corners and through the middles of the sides.The parallelogram has no lines of symmetry.
- Try some fold lines. Fold along a diagonal or along a line through the middle. The halves do not match.No fold line works.
- Write the answer. 0
Check. Try folding in several ways: the halves never fit. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The regular hexagon has 6 lines of symmetry.
- Count the lines. The number of lines of symmetry is 6.
- Write the answer. 6
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines of symmetry of each shape. The shapes with no lines of symmetry are the answer.
- Check each shape. Imagine folding it in different ways.ABCDEF
- Count the lines. Zero lines means no fold makes the halves match.A: no lines of symmetry
B: no lines of symmetry
C: 1 line of symmetry
D: no lines of symmetry
E: 4 lines of symmetry
F: no lines of symmetry - Choose. The shapes with no lines of symmetry are A, B, D and F.
Check. Each of these shapes has no fold that makes the halves match. ✓
Watch out. A parallelogram has no lines of symmetry, even though it looks balanced.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Count the lines of symmetry of each shape. Find the shape with exactly one line.
- Check each shape. Imagine folding it.ABCD
- Count the lines. A: 2 lines of symmetry
B: 1 line of symmetry
C: 3 lines of symmetry
D: no lines of symmetry - Choose. Only shape B has exactly one line.
Check. The kite has one line along its long diagonal. ✓
Watch out. Turning a shape does not change the number of lines.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror standing up the middle of the letter (a vertical line) and another lying across the middle (a horizontal line). If one half is the mirror image of the other, it is a line of symmetry.
- Look at the letter H. The red dashed lines are the lines of symmetry.
- Test the up-and-down (vertical) line. Do the left and right halves match?Yes.
- Test the across (horizontal) line. Do the top and bottom halves match?Yes.
- Count. The letter H has 2 lines of symmetry.
Check. Fold a copy of the letter along each line to check. ✓
Watch out. Look at the letter as a block shape.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror standing up the middle of the letter (a vertical line) and another lying across the middle (a horizontal line). If one half is the mirror image of the other, it is a line of symmetry.
- Look at the letter A. The red dashed lines are the lines of symmetry.
- Test the up-and-down (vertical) line. Do the left and right halves match?Yes.
- Test the across (horizontal) line. Do the top and bottom halves match?No.
- Count. The letter A has 1 line of symmetry.
Check. Fold a copy of the letter along each line to check. ✓
Watch out. Look at the letter as a block shape.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror standing up the middle of the letter (a vertical line) and another lying across the middle (a horizontal line). If one half is the mirror image of the other, it is a line of symmetry.
- Look at the letter Z. The red dashed lines are the lines of symmetry.
- Test the up-and-down (vertical) line. Do the left and right halves match?No.
- Test the across (horizontal) line. Do the top and bottom halves match?No.
- Count. The letter Z has 0 lines of symmetry.
Check. Fold a copy of the letter along each line to check. ✓
Watch out. Look at the letter as a block shape.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror standing up the middle of the letter (a vertical line) and another lying across the middle (a horizontal line). If one half is the mirror image of the other, it is a line of symmetry.
- Look at the letter C. The red dashed lines are the lines of symmetry.
- Test the up-and-down (vertical) line. Do the left and right halves match?No.
- Test the across (horizontal) line. Do the top and bottom halves match?Yes.
- Count. The letter C has 1 line of symmetry.
Check. Fold a copy of the letter along each line to check. ✓
Watch out. Look at the letter as a block shape.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror going up and down through the middle of each letter. Which letters have two halves that match?
- Test each letter. Check the vertical line (up and down).A: yes
D: no
E: no
H: yes
M: yes
N: no
T: yes
V: yes
W: yes
Z: no - Write the letters that match. A, H, M, T, V and W
Check. Fold a copy of each letter down the middle to check. ✓
Watch out. D has a line across the middle (horizontal), not up and down.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror going across the middle of each letter. Which letters have a top half that matches the bottom half?
- Test each letter. Check the horizontal line (across).A: no
D: yes
E: yes
H: yes
M: no
N: no
T: no
V: no
W: no
Z: no - Write the letters that match. D, E and H
Check. Turn the page on its side and fold again to check. ✓
Watch out. A has a vertical line only.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror along each possible line: up and down, across, and the two corner-to-corner lines. Check each one: does the shaded pattern match on both sides?
- Test the vertical line (up and down). Compare the left and right sides.Matches.
- Test the horizontal line (across). Compare the top and bottom.Matches.
- Test the two diagonal lines. Compare the two sides of each corner-to-corner line.The \ diagonal matches. The / diagonal matches.
- Count the lines. The red lines are the lines of symmetry.The pattern has 4 lines of symmetry.
Check. Fold along each red line: the shaded squares land on shaded squares. ✓
Watch out. Do not forget the diagonal lines.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror along each possible line: up and down, across, and the two corner-to-corner lines. Check each one: does the shaded pattern match on both sides?
- Test the vertical line (up and down). Compare the left and right sides.Matches.
- Test the horizontal line (across). Compare the top and bottom.Does not match.
- Test the two diagonal lines. Compare the two sides of each corner-to-corner line.The \ diagonal does not match. The / diagonal does not match.
- Count the lines. The red lines are the lines of symmetry.The pattern has 1 line of symmetry.
Check. Fold along each red line: the shaded squares land on shaded squares. ✓
Watch out. Do not forget the diagonal lines.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror along each possible line: up and down, across, and the two corner-to-corner lines. Check each one: does the shaded pattern match on both sides?
- Test the vertical line (up and down). Compare the left and right sides.Does not match.
- Test the horizontal line (across). Compare the top and bottom.Does not match.
- Test the two diagonal lines. Compare the two sides of each corner-to-corner line.The \ diagonal matches. The / diagonal does not match.
- Count the lines. The red lines are the lines of symmetry.The pattern has 1 line of symmetry.
Check. Fold along each red line: the shaded squares land on shaded squares. ✓
Watch out. Do not forget the diagonal lines.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Imagine a mirror along each possible line: up and down, across, and the two corner-to-corner lines. Check each one: does the shaded pattern match on both sides?
- Test the vertical line (up and down). Compare the left and right sides.Does not match.
- Test the horizontal line (across). Compare the top and bottom.Does not match.
- Test the two diagonal lines. Compare the two sides of each corner-to-corner line.The \ diagonal does not match. The / diagonal does not match.
- Count the lines. The red lines are the lines of symmetry.The pattern has 0 lines of symmetry.
Check. No line makes the pattern match. ✓
Watch out. Do not forget the diagonal lines.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The regular heptagon has 7 lines of symmetry.
- Count the lines. The number of lines of symmetry is 7.
- Write the answer. 7
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The regular octagon has 8 lines of symmetry.
- Count the lines. The number of lines of symmetry is 8.
- Write the answer. 8
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.
- Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.The red dashed lines are the lines of symmetry.
- Look for every line. Try lines through the corners and through the middles of the sides.The regular decagon has 10 lines of symmetry.
- Count the lines. The number of lines of symmetry is 10.
- Write the answer. 10
Check. Fold along each red line: the two halves fit exactly. ✓
Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the line of symmetry. Then say if it goes up and down (vertical), across (horizontal), or at a slant (sloping).
- Find the line of symmetry. It is the fold line that makes the two halves match.
- Look at the direction of the line. Vertical is straight up and down. Horizontal is straight across. Anything else slopes.The line is vertical.
- Write the answer. vertical
Check. Look at the picture: the red line is vertical. ✓
Watch out. The direction of the line changes when the shape is turned, but the number of lines stays the same.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the line of symmetry. Then say if it goes up and down (vertical), across (horizontal), or at a slant (sloping).
- Find the line of symmetry. It is the fold line that makes the two halves match.
- Look at the direction of the line. Vertical is straight up and down. Horizontal is straight across. Anything else slopes.The line is horizontal.
- Write the answer. horizontal
Check. Look at the picture: the red line is horizontal. ✓
Watch out. The direction of the line changes when the shape is turned, but the number of lines stays the same.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Find the line of symmetry. Then say if it goes up and down (vertical), across (horizontal), or at a slant (sloping).
- Find the line of symmetry. It is the fold line that makes the two halves match.
- Look at the direction of the line. Vertical is straight up and down. Horizontal is straight across. Anything else slopes.The line is sloping.
- Write the answer. sloping
Check. Look at the picture: the red line is sloping. ✓
Watch out. The direction of the line changes when the shape is turned, but the number of lines stays the same.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Each line of symmetry is a way to fold the square so that the halves match. Count the lines of symmetry.
- Find the lines of symmetry of a square. Fold along the middle lines and the diagonals.
- Count them. Each line is one different fold.4 lines
- Write the answer. Ravi can make 4 different folds.
Check. The square has 2 middle lines and 2 diagonals: 2 + 2 = 4. ✓
Watch out. Do not forget the two diagonal folds.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. A line of symmetry must make the two halves fit exactly. Test the diagonal of a rectangle.
- Look at what Ali says. Ali says a rectangle has 4 lines: 2 diagonals and 2 middle lines.Ali: 4 lines
- Test the middle lines. These two work. The halves match.Two lines of symmetry.
- Test a diagonal. Fold along it. The picture shows where the other half lands.The orange outline sticks out: the halves do not fit.
- Answer. Ali is wrong. A rectangle has 2 lines of symmetry.
Check. Only a square has its diagonals as lines of symmetry. ✓
Watch out. A rectangle is not a square, so its diagonals are not lines of symmetry.
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. A square has 4 equal sides and 4 lines of symmetry. A rhombus has 4 equal sides but only 2 lines.
- Try a square. 4 equal sides.4 lines of symmetry.
- Try a rhombus. 4 equal sides.2 lines of symmetry.
- Decide. Different shapes with four equal sides have different numbers of lines.The statement is sometimes true.
Check. The square has 4 lines and the rhombus has 2. ✓
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. A regular polygon has the same number of lines of symmetry as sides.
- Think about a regular pentagon. 5 sides.5 lines
- Think about a regular octagon. 8 sides.8 lines
- Decide. It works for every regular polygon.The statement is always true.
Check. Equilateral triangle: 3 sides, 3 lines. ✓
Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.
Method. Use the clues one at a time. After each clue, cross out the shapes that cannot be the answer. The shape that is left is the answer.
- Use the clue: “I have 4 sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: square, rectangle, rhombus, parallelogram, trapezium and kite.
Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - Use the clue: “My sides are not all the same length.” Cross out every shape that does not fit. Keep the ones that do.Keep: rectangle, parallelogram, trapezium and kite.
Cross out: square and rhombus. - Use the clue: “I have two lines of symmetry.” Cross out every shape that does not fit. Keep the ones that do.Keep: rectangle.
Cross out: parallelogram, trapezium and kite. - Write the answer. Only one shape fits every clue.The shape is the rectangle.
Check. Look at the rectangle: every clue is true for it. ✓
Watch out. Read every clue. One clue on its own often fits more than one shape.