Comparing and classifying shapes

​​In a nutshell

2D shapes, sometimes known as plane shapes, are flat and all have different properties. It is important to be able to classify them based on their properties.

Properties

A property is a quality that a shape has. Below is a list that highlights the key properties of shapes:

• Number of sides.
  
• Number of angles or corners.
  
• Length of sides.
• Types of angles (acute, obtuse, reflex or right-angle).
• Parallel and perpendicular lines.

Triangles

All triangles have three sides and three angles. However, different triangles have different properties depending on how they are drawn. A triangle could be:

• Equilateral - all three sides are the same and all three angles are the same.
  
• Isosceles - two sides and two angles are the same.
• Scalene - all sides and angles are different.
• Right-angled - one angle is 90 degrees (a right angle).

It is important to look carefully at the triangle and its properties in order to classify it correctly.

Quadrilaterals

A quadrilateral is a shape with four sides and four angles. Here are a few examples of quadrilaterals and their properties: 

​​sHAPE	pROPERTIES	dIAGRAM
Rectangle	Two pairs of equal sides. Angles all right angles (perpendicular lines). Two pairs of parallel lines.
Square	A special case of a rectangle. Sides all equal in length. Angles all right angles (perpendicular lines). Two pairs of parallel lines.
Trapezium	One pair of parallel lines. Two sets of equal angles.
Kite	Two pairs of equal sides. One pair of equal angles. No parallel lines.

Regular polygons

A regular polygon is a shape that has all equal sides and equal angles. Here are some examples of the most common regular polygons and their properties:

​​Shape	Properties	Diagram
Pentagon	Five equal sides and angles.
Hexagon	Six equal sides and angles. Three pairs of parallel lines.
Heptagon	Seven equal sides and angles.
Octagon	Eight equal sides and angles. Four pairs of parallel lines.

Irregular polygons

Irregular polygons are shapes that have sides and angles of different sizes. The left image below is a regular pentagon. The right image below is an irregular pentagon.

Tip: You can always identify a polygon by how many sides it has. For example, a pentagon is always a shape that has five sides, regardless of whether it is regular or irregular.