Chapter 7.1 & 7.2 Notes: The Pythagorean Theorem and its Converse

1. Chapter 7.1 & 7.2 Notes: The Pythagorean Theorem and its Converse Goal: To use the Pythagorean Theorem and its Converse.

2. Right Triangles: • In a right triangle, the side opposite the right angle is the longest side, called the hypotenuse. The other two sides are the legs of a right triangle. • Theorem 7.1 Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a2 + b2 = c2

3. Find the value of x. Leave your answer in simplest radical form. Ex.1: Ex.2: Ex.3: A 16-foot ladder rests against the side of the house, and the base of the ladder is 4 feet away. Approximately how high above the ground is the top of the ladder?

4. When the lengths of the sides of a right triangle are integers, the integers form a Pythagorean Triple. • Common Pythagorean Triples and Some of Their Multiples:

5. Ex.4: Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters. • Find the value of x. Leave your answer in simplified radical form. Ex.5: Ex.6:

6. Theorem 7.2 Converse of the Pythagorean Theorem: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. If c2 = a2 + b2, then ∆ABC is a right triangle.

7. Tell whether a triangle with the given side lengths is a right triangle. Ex.7: 5, 6, Ex.8: 10, 11, 14 Ex.9: 8 4

8. The Converse of the Pythagorean Theorem is used to determine if a triangle is a right triangle, acute triangle, or obtuse triangle. • If c2 = a2 + b2, then the triangle is a right triangle. • If c2 > a2 + b2, then the triangle is an obtuse triangle. • If c2 < a2 + b2, then the triangle is an acute triangle.

9. Determine if the side lengths form a triangle. If so, classify the triangle as acute, right, or obtuse. Ex.10: 15, 20, and 36 Ex.11: 6, 11, and 14 Ex.12: 8, 10, and 12 Ex.13: 4.3, 5.2, and 6.1