Pythagoras' theorem
In a nutshell
Pythagoras' theorem is very useful when trying to find the value for the third side of a rightangled triangle. Additionally, at this level, you may have to apply the formula to finding the distance between 2 points on a graph.
Recap
Pythagoras' theorem says that:
$a^2+b^2=c^2$
Where $a$ and $b$ are the two shorter sides of a rightangled triangle and $c$ is the hypotenuse.
Note: Pythagoras' theorem only works for a rightangled triangle. If there is no rightangle, then you cannot use Pythagoras' theorem.
Hypotenuse
The hypotenuse of a triangle is the longest side. For a rightangled triangle, the hypotenuse is always the side opposite the rightangle.
Distance between two points on a graph
You may be asked to find the distance between 2 given coordinates. Approaching these types of problems always requires the same method.
PROCEDURE
1.
 Do a quick sketch of the graph with the given coordinates and draw a rightangled triangle with the two points.

2.
 Find the lengths of the two shorter sides of the triangle.

3.
 Use Pythagoras' theorem to find the length of the hypotenuse of the triangle  this is the distance.

Example
Find the distance between the points $A (1,3)$ and $B(5,5)$.
First, make a quick sketch:
The length of the horizontal side is:
$5  (1) = 6$
The length of the vertical side is:
$3  (5) = 8$
The distance (labelled $d$) will then satisfy Pythagoras' theorem:
$6^2 + 8^2 = d^2$
$36+64=d^2$
$d^2 = 100$
$\underline{d = \sqrt{100} = 10}$