**Lengths of Sides in an Isosceles Right Triangle**

*****Remember that the you can find out if the triangle is a right triangle using the Pythagoream Theorem*

** Isosceles Right Triangle:** An

*isosceles right triangle*is a triangle with one angle equal to ninety degrees and each of the other two angles equal to forty five degrees.

**\begin{align*}a^2 + a^2 & = c^2\\
2a^2 & = c^2\\
\sqrt{2a^2} & = \sqrt{c^2}\\
a\sqrt{2} & = c\end{align*} a2+a22a22a2−−−√a2√=c2=c2=c2−−√=c**

**Relationship of Sides in a 30-60-90 Triangle**

**30-60-90 Triangle:** A ** 30-60-90 Triangle:** is a triangle with one angle equal to ninety degrees, one angle equal to thirty degrees, and one angle equal to sixty degrees.

**\begin{align*}s^2 + h^2 & = (2s)^2\\
s^2 + h^2 & = 4s^2\\
h^2 & = 3s^2\\
h & = s\sqrt{3}\end{align*} s2+h2s2+h2h2h=(2s)2=4s2=3s2=s3√**

**Special Triangle Ratios**

**Special Triangle:** A special triangle is a triangle that has particular internal angles that cause the sides to have a certain length relationship with each other.

What are some special triangles that can be identified?

The ratio of the sides of an isosceles right triangle is** \begin{align*}x:x:x\sqrt{2}\end{align*} x:x:x2√**

The ratio of the sides of a 30-60-90 right triangle is** \begin{align*}x:x\sqrt{3}:2x\end{align*} x:x3√:2x**