Geometric shapes: Types and properties

​​In a nutshell

Geometric shapes are structures made up of lines, curves and points. Geometric shapes, such as triangles and quadrilaterals, can be classified according to their properties.

Regular and irregular shapes

Shapes are regular if their sides are the same length. Irregular shapes have sides of different lengths. Below on the left is a regular pentagon. Below on the right is an irregular pentagon.

Note: All the interior angles of regular shapes are equal.

Triangles

There are four types of triangle:

• Equilateral - three equal sides and three equal angles (all 60$$\degree$$).​
  
• Isosceles -  two equal sides and two equal angles.
• Scalene - no equal sides and all angles different.
• Right-angled - one angle is a right angle (90$$\degree$$).

Note: In diagrams of shapes, lines of equal length are sometimes marked with dashes, and parallel lines are marked with arrows.

Quadrilaterals

Quadrilaterals are four-sided shapes. There are a number of variations, some of which are shown in the table below:

​​SHape name	properties	diagram
Square	All angles are 90$$\degree$$. All sides are equal in length. Opposite side are parallel.
Rectangle	All angles are 90$$\degree$$. Opposite sides are equal in length. Opposite sides are parallel.
Parallelogram	Diagonally opposite angles are equal. Opposite sides are equal in length. Opposite sides are parallel.
Rhombus	Diagonally opposite angles are equal. All sides are equal in length. Opposite sides are parallel.
Trapezium	One pair of opposite sides is parallel.

Tip: A rhombus can be thought of as a squashed square, and a parallelogram as a squashed rectangle.