Special Triangles in Geometry

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

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.

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

3a

a2

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 2n

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