What is a 45-45-90 triangle?
As you would have previously learnt, there are three types of triangles: equilateral, isosceles, and scalene. The 45-45-90 is an isosceles right triangle since it has two opposite sides of equal length and the angle between the two equal sides is 90°, but this triangle is special because it has some other unique properties. We call this the 45-45-90 triangle, because the triangle has the angles 45°, 45°, and 90° like so:

How to use this concept?
We can use this concept to simplify how to find certain quantities or lengths. For example, to begin we know that the ratio of the sides are 1:1:√2 and the ratio of the angles are 1:1:2. In addition, one of the key properties is that the hypotenuse (longest side of the triangle) is the length of the of either side times the square root of 2 (i.e. hyp = side x√2). Using this formula, if you know either one of the quantities, you can find the other quantity. For example, if I knew the length of the hypotenuse, we would divide hypotenuse by square root of two to find the length of the (equal) sides.

How to use this concept?
We can use this concept to simplify how to find certain quantities or lengths. For example, to begin we know that the ratio of the sides are 1:1:√2 and the ratio of the angles are 1:1:2. In addition, one of the key properties is that the hypotenuse (longest side of the triangle) is the length of the of either side times the square root of 2 (i.e. hyp = side x √2). Using this formula, if you know either one of the quantities, you can find the other quantity. For example, if I knew the length of the hypotenuse, we would divide hypotenuse by square root of two to find the length of the (equal) sides.
