Shape & Space
2D Shape Properties: Lines of Symmetry and Tessellation
3rd Class · 4th Class · 5th Class · 6th Class
- ✓By the end of this lesson students will be able to identify and draw lines of symmetry in 2D shapes.
- ✓By the end of this lesson students will be able to understand the concept of tessellation.
- ✓By the end of this lesson students will be able to identify shapes that tessellate and explain why.
- ✓By the end of this lesson students will be able to create simple tessellations using common shapes.
Key concepts
A line of symmetry is an imaginary line that divides a 2D shape into two identical halves. If you fold the shape along this line, both halves will match up perfectly, like a mirror image. Some shapes have no lines of symmetry, some have one, and some have many.
Tessellation (also called tiling) is when shapes fit together perfectly without any gaps or overlaps to cover a surface. Think of tiles on a floor or bricks in a wall. Shapes that tessellate can be repeated over and over again to fill a space completely.
Key facts to remember
- 1A line of symmetry divides a shape into two identical mirror-image halves.
- 2If you fold a shape along a line of symmetry, the two halves will match exactly.
- 3Some shapes have no lines of symmetry (e.g., a scalene triangle), some have one (e.g., an isosceles triangle), and some have many (e.g., a square has 4, a circle has infinite).
- 4Tessellation is when shapes fit together perfectly without any gaps or overlaps to cover a surface.
- 5Squares, rectangles, and equilateral triangles are common examples of shapes that tessellate.
- 6Regular hexagons also tessellate.
- 7Circles do not tessellate because they always leave gaps between them when placed side-by-side.
- 8Many irregular shapes can also tessellate.
Worked examples
Example 1
Draw a rectangle and show all its lines of symmetry. How many lines of symmetry does a rectangle have?
Answer
A rectangle has 2 lines of symmetry.
Remember to use a ruler to draw straight lines.
Example 2
Does an equilateral triangle tessellate? Explain your answer.
Answer
Yes, an equilateral triangle tessellates. This is because multiple equilateral triangles can fit together perfectly at their vertices (corners) without leaving any gaps or overlapping, allowing them to cover a flat surface completely.
Equilateral triangles are one of the three regular polygons that tessellate on their own (the others are squares and regular hexagons).
Example 3
Does a regular pentagon tessellate? Explain your answer.
Answer
No, a regular pentagon does not tessellate. When you try to fit regular pentagons together, they either leave gaps or overlap, meaning they cannot completely cover a flat surface without gaps or overlaps.
Only certain shapes have angles that add up to 360 degrees when placed around a point, which is necessary for tessellation.
Common mistakes
- ✗Drawing a line that cuts a shape in half but does not create two identical mirror images (e.g., a diagonal in a rectangle is not a line of symmetry).
- ✗Missing some lines of symmetry in a shape (e.g., forgetting the diagonal lines in a square).
- ✗Thinking a shape tessellates even if there are small gaps or overlaps between the shapes.
- ✗Confusing the idea of 'cutting a shape in half' with 'drawing a line of symmetry'.
Exam tips
- ★Always use a ruler and a sharp pencil when drawing lines of symmetry to ensure accuracy.
- ★To check for symmetry, imagine folding the shape along your proposed line. If the two halves don't match exactly, it's not a line of symmetry.
- ★When thinking about tessellation, draw a few of the shapes and try to fit them together like puzzle pieces to see if they leave gaps or overlap.
- ★Practice identifying and drawing lines of symmetry for a variety of 2D shapes.
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