1. The Pythagorean Theorem
5-7
The Pythagorean Theorem
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry

2. Objectives
TSW use the Pythagorean Theorem and its converse to solve problems.
TSW use Pythagorean inequalities to classify triangles.

3. Vocabulary
Pythagorean triple

4. The Pythagorean Theorem is probably the most famous mathematical relationship. As you learned in Lesson 1-6, The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
a2 + b2 = c2

5. A Pythagorean triple is a set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2

6. The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths.

7. You can also use side lengths to classify a triangle as acute or obtuse.

8. To understand why the Pythagorean inequalities are true, consider ∆ABC.

9. By the Triangle Inequality Theorem, the sum of any two side lengths of a triangle is greater
than the third side length.
Remember!