Constructing triangles
If we know the lengths of the three sides of a triangle, we can construct it on paper using a ruler and a pair of compasses.
The slideshow below shows how to do this construction. Use the left and right arrow buttons to move through the slideshow.
We could have worked out that this triangle was 'rightangled' by testing it with Pythagoras' theorem:
Squaring the two shorter sides and adding them together gives 225 and squaring the longest
side also gives 225, so Pythagoras' theorem is true for this triangle  it must be rightangled.
What about other triangles? What can we find out about other types of triangle using Pythagoras' theorem?
Types of angles in triangles
When considering the angles in triangles, there are three types of triangle: rightangled, obtuseangled and acuteangled.
A rightangled triangle has one 90° angle (the other two angles are acute).
An obtuseangled triangle has one obtuse angle (the other two angles are acute).
An acuteangled triangle has three acute angles.
The examples below show one of each type of triangle.
In each case the two shorter sides are marked a and b and the longest side is marked c.
Using the lengths of the sides to work out the type of triangle
From the diagram above, we can use the following method to calculate the type of triangle:
c² = a² + b²  rightangled triangle 
c² > a² + b²  obtuseangled triangle 
c² < a² + b²  acuteangled triangle 
(a) Triangle with sides 6cm, 7cm, and 8cm  
(b) Triangle with sides 5cm, 12cm, and 13cm  
(c) Triangle with sides 6cm, 11cm, and 14cm 
