2D shapes & symmetry
In this topic you will
- Explain symmetry and identify lines of symmetry.
- Identify, describe, sort, name, and sketch 2D shapes.
- Recognise 2D shapes in familiar everyday objects.
Key Words
- hexagon
- horizontal
- line of symmetry
- mirror image
- octagon
- pentagon
- polygon
- symmetry, symmetrical
- vertical
Show Definitions
- hexagon: A 2D polygon with six straight sides and six angles.
- horizontal: A direction or line that goes left to right, parallel to the horizon.
- line of symmetry: A line that divides a shape into two identical halves that match when folded or reflected.
- mirror image: The flipped reflection of a shape across a line, like the image seen in a mirror.
- octagon: A 2D polygon with eight straight sides and eight angles.
- pentagon: A 2D polygon with five straight sides and five angles.
- polygon: A closed 2D shape made from straight line segments.
- symmetry, symmetrical: A property where a shape can be split or reflected so the parts match exactly in size and shape.
- vertical: A direction or line that goes up and down, perpendicular to the horizon.
A $2$D shape is flat.
Something is symmetrical when it is the same on both sides.
A shape has symmetry if a line drawn down (vertical) or
across (horizontal) the middle shows that both sides of the
shape are exactly the same.
EXERCISES
$1$. Find the symmetrical shapes. Use a ruler to draw a line of symmetry on them.
👀 Show answer
The symmetrical shapes are the ones that can be split into two matching mirror halves:
- Top-left shape: yes (it has a vertical line of symmetry).
- Pink hexagon: yes (it has several lines of symmetry).
- Blue wavy shape: yes (it has a vertical line of symmetry).
- Blue teardrop: yes (it has a vertical line of symmetry).
$2$. Draw a pattern each side of the lines of symmetry to make them symmetrical. The first one is an example.
💡 Quick Math Tip
Mirror Image Check: When you draw or complete a symmetrical shape, imagine a mirror on the line of symmetry—the other side should be the exact reflected (mirror) image.
👀 Show answer
Answers will vary. The correct pattern is any drawing where the shapes on one side are a mirror image of the shapes on the other side across the blue line.
$3$. Draw the other half of these pictures to make them symmetrical.
👀 Show answer
Answers will vary. Complete each picture by drawing the missing half as the reflection of the given half across the blue line (each point the same distance from the line on both sides).
$4$. Draw a symmetrical pattern using these shapes. Use $1$ line of symmetry. Your pattern can have a vertical or horizontal line of symmetry.
💡 Quick Math Tip
Folding Test for Symmetry: A line of symmetry is a line you can fold along so both halves match exactly. If the two sides do not line up perfectly, it is not a line of symmetry.
👀 Show answer
Answers will vary. A correct pattern is any arrangement where every shape has a matching mirror-image shape on the other side of the chosen line of symmetry (vertical or horizontal).
$5$. Draw $3$ objects that match these shapes. The first one is an example.
💡 Quick Math Tip
Quarters Make a Whole: When you see three-quarters $\frac{3}{4}$, remember that adding one more quarter $\frac{1}{4}$ completes the whole because $\frac{3}{4} + \frac{1}{4} = 1$.
👀 Show answer
Examples (any sensible matches are correct):
- Circle: clock, coin, plate.
- Square: floor tile, sticky note, chessboard square.
- Triangle: pizza slice, triangular road sign, pennant flag.
- Hexagon: hex nut, honeycomb cell, bolt head.
- Rectangle: book, door, phone screen.
$6$. Fill the triangles with small triangles and the squares with small squares. Fill the pentagons with small dots, the hexagons with large dots and the octagons with stripes.
Sort the patterned shapes into the Carroll diagram.
Draw $2$ shapes of your own and put them in the Carroll diagram.
👀 Show answer
Patterns:
- Triangles: small triangles.
- Squares: small squares.
- Pentagons: small dots.
- Hexagons: large dots.
- Octagons: stripes.
Carroll diagram sorting:
- Has square corners & Not more than $5$ sides: the square.
- Does not have square corners & Not more than $5$ sides: the triangle (and the pentagon if you include $5$ sides in “not more than $5$ sides”).
- Does not have square corners & $5$ or more sides: pentagon, hexagon, octagon.
- Has square corners & $5$ or more sides: none of the given shapes.
Your $2$ shapes: answers will vary. To fill the empty group, you could draw a shape with $5$ or more sides that has square corners (right angles).
$7$. Colour the rectangles. How many rectangles can you find?
👀 Show answer
There are $6$ rectangles.
$8$. How many different ways can you turn the triangle so that it looks different every time?
Draw round the shape to show the different ways.
👀 Show answer
There are $3$ different ways (each turn puts a different corner at the top).
$9$. Can you turn a circle so that it looks different?
Explain your answer.
👀 Show answer
No. A circle looks the same after any turn because it is the same all the way around, so rotating it does not change how it looks.
Think like a Mathematician
Task: Use up to $10$ squares to make different symmetrical shapes.
Rules:
- Work independently.
- Always place the squares edge to edge (no corners touching only).
- Draw $2$ different designs.
- Use shape and colour to show the symmetry.
Method:
- Choose a line of symmetry for your first design (vertical or horizontal).
- Place squares on one side of the line.
- Add matching squares on the other side so the design is a mirror image.
- Colour matching squares the same colour to show the symmetry clearly.
- Repeat steps $1$–$4$ to make a second, different symmetrical design (still using up to $10$ squares).
Check your work:
- If you fold your design along the line of symmetry, the two halves should match exactly.
- Every square on one side should have a partner square the same distance from the line on the other side.