1. THE PYTHAGOREAN THEOREM

2. PYTHAGOREAN THEOREM

3. REAL LIFE EXAMPLE The following is a rule of thumb for safely positioning a ladder: The distance from the bottom of the ladder to the wall should be one-fourth of the length of the ladder. Thus, the bottom of a 16-foot ladder should be 4 feet from the wall. How far up the wall will the ladder reach?

4. EXAMPLE 2 A plowed field is in the shape of a triangle. If the sides have the lengths shown in the figure, is the field a right triangle?

5. PYTHAGOREAN INEQUALITIES

6. PRACTICE A triangle has lengths of 7 inches, 8 inches, and 12 inches. Is the triangle right, obtuse or acute? 1.Which length is the hypotenuse? 2.How do you know? 3.What letter represents the hypotenuse, a, b or c? 4.Which side is a? Which side is b? Does it matter? 5.Set up the statement (equation/inequality) 6.Is c 2 equal to, bigger or smaller than a 2 + b 2 7.What type of triangle is this?

7. MORE PRACTICE The sides for the three triangles are given. Label each as acute, right, or obtuse. 1. 14 in., 7 in., 9 in. 2.2.5 cm, 6 cm, 6.5 cm 3.2 ft, 3 ft, 3.5 ft