1. Topic 10 – Lesson 9-1 and 9-2

2. Objectives Define and identify hypotenuse and leg in a right triangle Determine the length of one leg of a right triangle given the hypotenuse and a leg Apply the Pythagorean Theorem and its converse to real-world situations Use Pythagorean triples to determine the length of a leg or the hypotenuse of a right triangle

3. In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called legs. In the figure at right, a and b represent the lengths of the legs, and c represents the length of the hypotenuse. LEGS HYPOTENUSE c a b

4. There is a special relationship between the lengths of the legs and the length of the hypotenuse. This relationship is known today as the Pythagorean Theorem.

5. In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse The Theorem a 2 + b 2 = c 2. c a b

6. Example: In a right triangle, the length of one leg is 6 cm and the length of the other leg is the square root of 13 cm. Find the length of the hypotenuse. The Pythagorean theorem Take the square root of both sides in order to get c The length of the hypotenuse is 7 cm

7. It is a set of positive integer that satisfies the rule a 2 + b 2 = c 2 where c is the measure of the hypotenuse There are some examples 5, 12, 13 3, 4, 5 9, 40, 41 5 13 12 3 5 4 9 41 40

8. If the lengths of the three sides of a triangle satisfy the Pythagorean equation, them the triangle is a right triangle

9. The sides of a triangle measure 8, 15, and 17. Is the triangle a right triangle? Example: According to the converse of the Pythagorean theorem, if a, b, and c are the lengths of sides of a triangle and if a 2 + b 2 = c 2, then the triangle is a right triangle. Substituting 8 for a, 15 for b and 17 for c ?