Isoceles Triangle: Is a triangle that has two sides that are equal length.

Scalene traingle: A triangle that has that all different sides

Right triangle: A triangle that is made up of a right angle.

The ** Pythagorean Theorem** is a mathematical relationship between the sides of a right triangle, given by \begin{align*}a^2 + b^2 = c^2\end{align*}, where \begin{align*}a\end{align*}, \begin{align*}b\end{align*}, and \begin{align*}c\end{align*} are lengths of the triangle.

**Lengths of Triangle Sides Using the Pythagorean Theorem:**

To find the length of one side of a triangle, given the other two sides, use the formula a^{2}+ b^{2}= c^{2}

**Identifying Sets of Pythagorean Triples**

*Pythagorean Triple*: a set of three integers that make up the three sides of a right triangle for which the Pythagorean Theorem holds true

*Examples of Pythagorean Triples:*

3, 4, 5

5, 12, 13

7, 24, 25

11, 60, 61

**Using Pythagorean Theorem to Classify Triangles:**

If a^{2} + b^{2}= c^{2} then it is a right triangle. Knowing this, what can you infer if a^{2} + b > c^{2} or if a^{2} + b^{2} < c^{2} ?

**Using Pythagorean Theorem to Determine Distance:**

We can use the Pythagorean Theorem to derive the Distance Formula.

To find the distance between two points, (x_{1}, y_{1}), and (x_{2}, y_{2}), simply plug it into the following formula.

\begin{align*}\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2} = d\end{align*}