# Properties of 2D Shapes

## What is a 2D shape?

A 2D shape is a flat shape. They are shapes that only have 'two-dimensions' which means that they only have length and width. This is in contrast to 3D (three-dimensional) shapes which also have height. ## 2D Shapes Properties - Important Vocabulary

Before we look at examples of 2D shapes, let's begin by unpicking their properties. Knowing what the vocabulary means is really important for children when they come to describing the properties of 2D shapes.

The side of a 2-D shape is the line that forms the outline of the shape. Sides can be straight or curved. A line is another word for a side.

The corner of a 2-D shape is the point where two sides meet. A corner is also called a vertex, the plural of vertex is vertices.

A curved line is not straight. It bends.

A straight line does not have a bend or curve.

A horizontal line goes from left to right (or right to left) across a page. Horizontal lines are parallel to the horizon.

A vertical line goes from top to bottom (or bottom to top) of a page. Vertical lines are perpendicular to the horizon.

Parallel lines travel in the same direction and are always the same distance apart. They never meet.

Perpendicular lines intersect at a right angle.

The intersect is the point where two lines meet.

A regular 2-D shape’s sides and angles are all equal. For example, all the angles in a regular triangle equal 60º.

An irregular 2-D shape has sides and angles of differing sizes.

### Polygon

A polygon is a 2-D shape with straight sides. The sides must be straight and closed. Polygons can have any number of sides. Triangles and squares are polygons. A polygon with 10 sides is called a decagon. A polygon with 100 sides is called a hectogon. A polygon with 1000 sides is called a chiligon. A polygon with 1 billion sides is called a gigagon.

### Geometric shapes

Geometric shapes are regular shapes. Most geometric shapes have straight lines, angles and points. The two exceptions to this rule are circles and semi-circles.

The ten basic geometric 2D shapes are:

• Circle
• Triangle
• Semi-circle
• Square
• Rectangle
• Parallelogram
• Rhombus
• Trapezium
• Kite
• Polygons

### Elliptical shape

An elliptical shape is an elongated circle that has been stretched into an oval. Not every oval is an ellipse.

## 2D Shapes Properties - Activity Ideas

1. Shape sorting - giving children a collection of 2D shapes and asking them to sort them by number of sides, vertices or type can be a really useful activity. Make sure to include a range of different versions of each shape so that children used to seeing both regular and irregular versions of the shapes. Also make sure to show 2D shapes in different orientations - just because the rectangle is 'slanted' doesn't mean it isn't still a rectangle!

2. Shape riddles - Children could be asked to identify a 2D shape from a description of its properties. Alternatively, they could write their own riddles for each other, trying to use the correct vocabulary. You could give children a word bank with the vocabulary you want them to include in their riddles.

3. Spot the Shape! Children could be asked to go on a shape hunt around the classroom or school. Perhaps provide them with a checklist or table in which to record the shapes they find.

4. Spot the difference - Show children 2 shapes on the board and ask them to state as many differences as they can between them. This is a really good way to get them to use the vocabulary associated with 2D shape so be sure to have a word bank visible for children to refer to.

5. Make it! Why not get your class to make 2D shapes from art straws. By physically making the shapes and talking about their properties, children are much more likely to remember them.

6. Take it outside! Children love being outside so why not set up a scavenger hunt type activity. You could print out images of 2D shapes and pin them up around the playground, numbering them. Then, children could see how many they can find, recording the name of each one they find on a sheet of paper e.g. 1 = triangle 2 = circle 3 = regular hexagon 4 = irregular octagon etc.

## 2D Shapes Properties: Circles and Semi-Circles

A circle is a 2D shape that has one curved side. Circles are completely round as each point on its curved side is an equal distance from the centre of the circle. Circles have no vertices.

• A circle is a two-dimensional geometric shape.
• A circle has one side.
• A circle has one curved side.
• A circle has no vertices.
• The outside of a circle is called the circumference.
• All points on the circumference of a circle are the same distance from the centre of the circle. This distance is called the radius.
• A circle has an infinite number of lines of symmetry.

A semi-circle is half of a circle. It therefore has two sides, one of which is curved and one which is straight.

• A semicircle is a two-dimensional shape that forms half of a circle.
• A semicircle has two sides.
• A semicircle has one curved side and one straight side.
• A semicircle has two vertices.
• A semicircle has one line of symmetry.

## 2D Shapes Properties: Triangles

A triangle is a 2D shape that has three straight sides and three vertices.

• A triangle is a two-dimensional geometric shape.
• A triangle has three sides.
• A triangle has three straight sides.
• A triangle has three vertices.
• A triangle is a polygon.
• The sum of all the angles of a triangle is 180º.

There are different types of triangle:

1. Equilateral triangles - triangles which have three sides of equal length and three equal angles. Each angle will be 60 degrees.

2. Isosceles triangles - triangles which have two sides of equal length and two angles the same size.

3. Scalene triangles - triangles with no sides of equal length and no angles that are the same size.

4. Right-angled triangles - Triangles that contain a right-angle.

Quadrilaterals are shapes which have four straight sides and four vertices.

• A quadrilateral is a two-dimensional geometric shape.
• A quadrilateral has four sides.
• A quadrilateral has four straight sides.
• A quadrilateral has four vertices.
• There are six special quadrilaterals: square, rectangle, parallelogram, rhombus, trapezium, and kite.
• A quadrilateral is a polygon.

There are many different types of quadrilateral:

1. Squares - A square has four sides of equal length and four right angles.

• A square is a two-dimensional geometric shape.
• A square has four sides.
• A square has four straight sides.
• A square’s sides are all the same length.
• A square’s opposite sides are parallel.
• A square has four vertices.
• A square’s vertices are all the same size. The vertices are all 90º.
• All squares are rectangles but not all rectangles are squares.
• The sum of all the angles of a square is 360º. 90º + 90º + 90º + 90º = 360º
• A square is a polygon.

2. Rectangles - A rectangle has for sides and four right angles. Opposite sides of a rectangle are the same length, with one pair being longer than the other pair.

• A rectangle is a two-dimensional geometric shape.
• A rectangle has four sides.
• A rectangle has four straight sides.
• A rectangle has two sets of sides that are the same length.
• A rectangle’s opposite sides are parallel.
• A rectangle has four vertices.
• A rectangle’s vertices are all the same size. The vertices are all 90º.
• The sum of all the angles of a rectangle is 360º. 90º + 90º + 90º + 90º = 360º
• A rectangle is a polygon.

3. Kites - Kites have two pairs of sides. These pairs are of equal length and they are adjacent to each other. Where these two pairs meet, the angles are equal.

• A kite is a two-dimensional geometric shape.
• A kite has four sides.
• A kite has four straight sides.
• A kite has two pairs of sides that are the same length.
• A kite has four vertices.
• A kite has one pair of equal angles.
• A kite is a polygon.

4. Parrallelogram - A parrallelogram has opposite sides that are both parrallel and equal in length. Opposite angles are also the same.

• A parallelogram is a two-dimensional geometric shape.
• A parallelogram has four sides.
• A parallelogram has four straight sides.
• A parallelogram has two pairs of sides that are the same length.
• A parallelogram’s opposite sides are parallel.
• A parallelogram has four vertices.
• A parallelogram has two pairs of angles that are all the same size.
• Lines drawn joining the opposite angles of a parallelogram bisect each other.
• A parallelogram is a polygon.

5. Trapezium - A trapezium is a type of quadrilateral that has one pair of opposite sides that are parrallel with one another.

• A trapezium is a two-dimensional geometric shape.
• A trapezium has four sides.
• A trapezium has four straight sides.
• A trapezium has one pair of parallel sides.
• A trapezium has four vertices.
• A trapezium is a polygon.
• A trapezium is sometimes called a trapezoid.

## 2D Shapes Properties: Pentagons, Hexagons, Heptagons, Octagons

Pentagons - Pentagons have five sides and five vertices.

• A pentagon is a two-dimensional geometric shape.
• A pentagon has five sides.
• A pentagon has five straight sides.
• A pentagon has five vertices.
• The word pentagon comes from the ancient Greek words pente meaning five and agon meaning angle.
• A pentagon is a polygon.

Hexagons - Hexagons have six sides and six vertices.

• A hexagon is a two-dimensional geometric shape.
• A hexagon has six sides.
• A hexagon has six straight sides.
• A hexagon has six vertices.
• The word hexagon comes from the ancient Greek words héx meaning six and agon meaning angle.
• A hexagon is a polygon.

Heptagons - Heptagons have seven sides and seven vertices.

• A heptagon is a two-dimensional geometric shape.
• A heptagon has seven sides.
• A heptagon has seven straight sides.
• A heptagon has seven vertices.
• A heptagon is also known as a septagon.
• The word heptagon comes from the ancient Greek words heptá meaning seven and agon meaning angle.
• The word septagon comes from the Latin word sept meaning seven and the ancient Greek word agon meaning angle.
• A heptagon is a polygon.

Octagons - Octagons have eight sides and eight vertices.

• An octagon is a two-dimensional geometric shape.
• An octagon has eight sides.
• An octagon has eight straight sides.
• An octagon has eight vertices.
• The word octagon comes from the ancient Greek words okta meaning eight and agon meaning angle.
• An octagon is a polygon.

## 2D Shapes Properties: Nonagons, Decagons, Hendecagons

Nonagons - Nonagons have nine sides and nine vertices.

• A nonagon is a two-dimensional geometric shape.
• A nonagon has nine sides.
• A nonagon has nine straight sides.
• A nonagon has nine vertices.
• A nonagon is also known as an enneagon.
• The word nonagon comes from the Latin words nonus meaning nine and the ancient Greek word agon meaning angle.
• The word enneagon comes from ancient Greek meaning nine corners.
• A nonagon is a polygon.

Decagons - Decagons have ten sides and ten vertices.

• A decagon is a two-dimensional geometric shape.
• A decagon has ten sides.
• A decagon has ten straight sides.
• A decagon has ten vertices.
• The word decagon comes from the ancient Greek words déka meaning ten and the agon meaning angle.
• A decagon is a polygon.

Hendecagons - Hendecagon have eleven sides and eleven vertices.

• A hendecagon is a two-dimensional geometric shape.
• A hendecagon has eleven sides.
• A hendecagon has eleven straight sides.
• A hendecagon has eleven vertices.
• The word hendecagon comes from the ancient Greek words hendéka meaning eleven and the agon meaning angle.
• A hendecagon is a polygon.

## 2D Shapes Properties: Dodecagons, Triecagons, Tetradecagons

Dodecagons - Dodecagons have tweleve sides and tweleve vertices.

• A dodecagon is a two-dimensional geometric shape.
• A dodecagon has tweleve sides.
• A dodecagon has twelve straight sides.
• A dodecagon has twelve vertices.
• The word dodecagon comes from the English words dodeca meaning twelve and the gon meaning angles. The word dodeca comes from the Ancient Greek word dōdeka. The word gon comes from the Ancient Greek word gōnos.
• A dodecagon is a polygon.

Tridecagons - Tridecagons have thirteen sides and thirteen vertices.

• A tridecagon is a two-dimensional geometric shape.
• A tridecagon has thirteen sides.
• A tridecagon has thirteen straight sides.
• A tridecagon has thirteen vertices.
• A tridecagon is a polygon.

• A tetradecagon is a two-dimensional geometric shape.
• A tetradecagon has fourteen sides.
• A tetradecagon has fourteen straight sides.
• A tetradecagon has fourteen vertices.
• A tetradecagon is a polygon.

## 2D Shapes KS1

Here is what the National Curriculum says about teaching geometry in Year 1:

Pupils should be taught to:

• recognise and name common 2-D and 3-D shapes, including:
• 2-D shapes [for example, rectangles (including squares), circles and triangles]
• 3-D shapes [for example, cuboids (including cubes), pyramids and spheres]

Here is what the National Curriculum says about teaching geometry in Year 2:

Pupils should be taught to:

• identify and describe the properties of 2-D shapes, including the number of sides, and line symmetry in a vertical line
• identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
• identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
• compare and sort common 2-D and 3-D shapes and everyday objects

## 2D Shapes KS2

Here is what the National Curriculum says about teaching geometry in Year 3:

Pupils should be taught to:

• draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
• recognise angles as a property of shape or a description of a turn
• identify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle
• identify horizontal and vertical lines and pairs of perpendicular and parallel lines

Here is what the National Curriculum says about teaching geometry in Year 4:

Pupils should be taught to:

• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
• identify acute and obtuse angles and compare and order angles up to 2 right angles by size
• identify lines of symmetry in 2-D shapes presented in different orientations
• complete a simple symmetric figure with respect to a specific line of symmetry

Here is what the National Curriculum says about teaching geometry in Year 5:

Pupils should be taught to:

• identify 3-D shapes, including cubes and other cuboids, from 2-D representations
• know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• draw given angles, and measure them in degrees (°)
• identify:
• angles at a point and 1 whole turn (total 360°)
• angles at a point on a straight line and half a turn (total 180°)
• other multiples of 90°
• use the properties of rectangles to deduce related facts and find missing lengths and angles
• distinguish between regular and irregular polygons based on reasoning about equal sides and angles

Here is what the National Curriculum says about teaching geometry in Year 6:

Pupils should be taught to:

• draw 2-D shapes using given dimensions and angles
• recognise, describe and build simple 3-D shapes, including making nets
• compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
• illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles