This document discusses special right triangles in geometry. There are two main special right triangles: the 30-60-90 triangle, where the angles are 30, 60, and 90 degrees and the side lengths have a specific ratio, and the 45-45-90 triangle, where two angles are 45 degrees and the third is 90 degrees, with the two legs having equal lengths. Special right triangles have properties that allow calculating unknown side lengths given certain known values due to consistent side length ratios in each type of triangle.

1. Special Triangles in Geometry

2. What Makes a Triangle Special? Special triangles refer to triangles with one 90 degree angle Triangles are all made of two legs and the hypotenuse which is always opposite the 90 degree angle The great thing about special triangles is that the relationship between the sides is always constant for a given type of triangle

3. Opposite the Angle? The opposite angle can be seen by drawing a line cutting through the angle to the other side of the triangle. 90 degree angles are noted by a small square As seen here the opposite in this case is the hypotenuse also, but only because it is opposite of the 90 degree angle.

4. 30-60-90 The 30-60-90 can easily be distinguished from the other special triangle by the three noticeably different angles. There are two legs in the picture. The letter a notates the length of one leg and given this length, the length of the other leg is found by multiplying Hypotenuse length is equal to

5. 45-45-90 The other special triangle is a 45-45-90 and is easy to distinguish due to the equal side length of the two legs Given a leg length of n, the other leg will be the same length and the hypotenuse will always be

6. References Main Page Background http://www.desktopwallpaperhd.com/wallpapers/6/5498.jpg 30-60-90 Triangle http://upload.wikimedia.org/wikipedia/commons/4/45/30-60-90_triangle.jpg 45-45-90 Triangle http://www.onlinemathlearning.com/image-files/special-rt-triang-454590-1.gif