How to remember the 45 - 90 - 45 rule

How to remember the ratio of the sides is 1,`root()2`, 1

It's also important to remember that starting with 45° and a right angled triangle the ratio of the length of the sides are:

Visualise a square, of unit length 1, divided in half by a diagonal.

This creates a 45 - 90 - 45 right angled triangle.

Now apply Pythagoras theorem which states the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

i.e. `a^2+b^2=c^2`

With the two shortest sides being 1 unit long the hypotenuse is.

`1^2+1^2=c^2`

`1+1=c^2`

`2=c^2`

`root()2=c`

The hypotenuse is `root()2` long hence:

Or in any length ratio.