Define common 2D shapes
A 2D shape is flat, so we describe it using sides and corners.
3 sides3 corners
4 sides4 cornersopposite sides equal
6 sides6 corners
Corners and vertices mean the same idea in 2D, but sides are only used for flat shapes.
Year 7
Shape properties, polygons, line and rotational symmetry
Identify line and rotational symmetry, define key 2D and 3D shape properties, and name polygons from 5 to 10 sides.
Lesson overview
Geometry - shape properties and symmetry
Geometry is not only about drawing shapes. We also describe what makes a shape what it is. A 2D shape is flat and can be described by its sides and corners. A 3D shape is solid and can be described by faces, edges and vertices. Polygon names come from the number of sides, and symmetry tells us whether a shape matches itself by reflection or rotation.
Define common 3D shapes
A 3D shape is solid, so we describe it using faces, edges and vertices.
6 faces12 edges8 vertices
6 faces12 edges8 vertices
2 flat faces2 edges0 vertices
1 flat face1 edge1 vertex
1 curved surface0 edges0 vertices
5 faces9 edges6 vertices
Curved surfaces matter too, especially for cones, cylinders and spheres.
Polygon names from 5 to 10 sides
A polygon is a closed 2D shape with straight sides. A regular polygon also has equal sides and equal angles.
5 sides5 equal sides5 equal angles
6 sides6 equal sides6 equal angles
7 sides7 equal sides7 equal angles
8 sides8 equal sides8 equal angles
9 sides9 equal sides9 equal angles
10 sides10 equal sides10 equal angles
All polygons are 2D, closed and made only from straight sides. Regular ones also have matching sides and angles.
Symmetry helps classify shapes
A rectangle has 2 lines of symmetry and rotational symmetry of order 2, while a square has 4 lines and order 4.
| Shape | Lines of symmetry | Rotational symmetry |
|---|---|---|
| Rectangle | 2 | order 2 |
| Square | 4 | order 4 |
| Regular pentagon | 5 | order 5 |
The regular version of a polygon has more symmetry because all sides and angles match.
Worked example
Describe the properties of a regular pentagon.
5 sides5 equal sides5 equal angles
| Property | Value |
|---|---|
| Lines of symmetry | 5 |
| Rotational symmetry | order 5 |
- A pentagon is a polygon with 5 straight sides.
- Because it is regular, all 5 sides and all 5 angles are equal.
- Each matching section gives a mirror line through the centre, so there are 5 lines of symmetry.
- Turning it by one fifth of a full turn matches it again, so the rotational symmetry is order 5.
Try it
Use the shape definition first, then decide which property the question is asking for.
Question 1
How many sides does an octagon have?
8 sides8 equal sides8 equal angles
Question 2
Which solid has 6 faces, 12 edges and 8 vertices?
6 faces12 edges8 vertices
2 flat faces0 vertices
1 vertex
Question 3
Which statement is correct about a polygon?
joins up
flat
no curves
Question 4
What is the order of rotational symmetry of a square?
| Turn | Match? |
|---|---|
| 90 deg | yes |
| 180 deg | yes |
| 270 deg | yes |
Question 5
Which polygon name matches 10 sides?
9 sides
10 sidesregular form has equal sides
7 sides
Common mistakes
Watch for these when working through the lesson.
- Mixing up sides and edges, or corners and vertices.
- Calling a curved solid a polygon.
- Counting a line that does not split the shape into exact mirror halves.
- Forgetting that polygon names depend on the number of sides.
Related topics
These ideas fit closely with this lesson.
- Measure and draw angles accurately.
- Perimeter and area of rectangles, triangles and parallelograms.
- Generate and explain sequences.