1. 8-1: The Pythagorean Theorem and its Converse

2. The Pythagorean Theorem
In words:
As an equation:

3. Pythagorean Triples
A set of nonzero whole numbers a, b, and c that satisfy the equation 𝑎 2 + 𝑏 2 = 𝑐 2 is called a Pythagorean triple
Example: 3, 4, 5 or 8, 15, 17

4. Pythagorean Triples
The length of the hypotenuse of a right triangle is 25 and one leg has a length of 10. Do the lengths of the sides form a Pythagorean triple?
Do the sides of triangle ABC form a Pythagorean triple?

5. Converse of the Pythagorean Theorem
Write the converse of the Pythagorean theorem:

6. Converse of the Pythagorean Theorem
A triangle has sides of lengths 16, 48, and 50. Is it a right triangle?
Is this triangle a right triangle?

7. Side Measures of Obtuse and Acute Triangles
You will use GeoGebra to explore the measures of the side lengths of obtuse and acute triangles.

8. Your Rules:
What is the rule for the relationship between obtuse triangles’ side lengths?
What is the rule for the relationship between acute triangles’ side lengths?

9. Ticket out of class:
Please put your name on your paper.

10. Ticket out of class: Find the value of x. Find the value of x.
The lengths of the sides of a triangle are 5cm, 8cm, and 10cm. Is the triangle acute, right, or obtuse?