1. 8.1 Pythagorean Theorem and Its Converse
If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
The hypotenuse is ALWAYS the biggest side of the right triangle.
The hypotenuse is ALWAYS located opposite from the right angle.

2. Finding the Length of the Hypotenuse
What is the length of the hypotenuse in Triangle ABC?

3. Simplest Radical Form Simplify
To simplify a number, find numbers that go into the larger number that are perfect squares.
Example: 4, 9, 16, 25, 36, 49, etc….

4. Simplest Radical Form
Simplify

5. Finding the Length of the Leg
What is the value of x? Express your answer in simplest radical form.
Remember, the legs can go in for either a or b.
The hypotenuse must always be letter c.

6. Converse of the Pythagorean Theorem
If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
We use the converse of the Pythagorean Theorem to PROVE triangles are right triangles.

7. Pythagorean Triples
A Pythagorean triple is a set of nonzero whole numbers, a, b, and c that always satisfy the equation a² + b² = c².
Some common Pythagorean Triples:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

8. Classifying Right Triangles as Obtuse or Acute
Theorem Obtuse – If the square of the length of the longest side of a triangle is GREATER THAN the sum of the squares of the lengths of the other two sides, then the triangle is OBTUSE.
Theorem Acute – If the square of the length of the longest side of a triangle is LESS THAN the sum of the squares of the lengths of the other two sides, then the triangle is ACUTE.

9. Classifying a Triangle
A triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right?
c² ___ a² + b²
14² ___ 6² + 11²
196 ___
196 > 157
The triangle is obtuse.