2. Lesson 5-7 Use the Pythagorean Thm 1 Identify the Pythagorean triples 2 Use the Pythagorean inequalities to classify ∆s 3

3. Use the Pythagorean Theorem States that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. The Pythagorean Theorem Leg (a) Leg (b) Hypotenuse (c) a2a2 +b2b2 =c2c2 EXAMPLE 1 Find the length of the missing side c 5 12 Write the formula a 2 + b 2 = c 2 Substitute in the side lengths 5252 +12 2 = c2c2 25+144 = c2c2 169 = c2c2

4. A set of three nonzero whole numbers that satisfy a 2 + b 2 = c 2 The Pythagorean Triple EXAMPLE 2 Find the length of the missing side. Tell if the sides form a Pythagorean triple. Explain 12 4 b Write the formula a 2 + b 2 = c 2 Substitute in the side lengths 4242 +b2b2 = 12 2 16+b2b2 =144 b2b2 = –16 b2b2 =128 b is not a whole number ∴ they do not form A Pythagorean Triple Identify the Pythagorean triples 2

5. In ∆ABC, Pythagorean inequalities Theorem Use the Pythagorean inequalities to classify ∆s 3 If c 2 > a 2 + b 2, then ∆ABC is an obtuse ∆ If c 2 < a 2 + b 2, then ∆ABC is an Acute ∆ If c 2 = a 2 + b 2, then ∆ABC is a Right ∆ EXAMPLE 3 Tell if the measures can be the side lengths of a ∆. If so classify the ∆ as acute, obtuse or right 1)7, 12, 16 Obtuse Triangle 2)3, 2.1, 5.23)11, 18, 21 Checking c2c2 a2a2 + b2b2 16 2 12 2 + 7272 256144+49 256193> ∴ Obtuse ∆ Checking 3+2.15.2< ∴ They do not form a ∆ Checking c2c2 a2a2 + b2b2 21 2 18 2 + 11 2 441324+121 441445 ∴ Acute ∆ <

6. Homework Pg 364 - 367 2, 3, 6, 7, 8, 9, 10, 13, 14, 16, 20, 22, 24, 30, 32, 34, 35, 38, 40, 42, and 43

7. Find the perimeter and the area of each figure. 17 8 x Step1: find x 8 2 + x 2 = 17 2 x 2 = 289 – 64 x 2 = 225 x = √225 =15 15 Step2: find the perimeter Perimeter = 8 + 17 + 15 = 40 Step3: find the Area Area = (h ● b) / 2 = (8 ● 15) / 2 = 120 / 2 = 60

8. Find the perimeter and the area of the following figure. Step1: find x 8 12 x 44 4 2 + x 2 = 12 2 x 2 = 144 – 16 x 2 = 128 x = √128 = 8√2 Step2: find the perimeter Perimeter = 12 + 12 + 8 = 32 Step3: find the Area Area = (h ● b) / 2 = (8√2 ● 8) / 2 = 64√2 / 2 = 32√2

9. 9 15 Find the value of x. Give your answer in radical form x y 13 III Use ∆I to find y 9 2 + y 2 = 15 2 y 2 = 15 2 – 9 2 y 2 = 225 – 81 y 2 = 144 y = √144 y = 12 Use ∆II to find x 9 2 + 13 2 = x 2 x 2 = 13 2 + 9 2 x 2 = 169 + 81 x 2 = 250 x = √250 = 5√10 12 25

10. 17 8 x15 12 5 x 13 Tell if the measures can be the side lengths of a ∆. If so classify the ∆ as acute, obtuse or right 1)3, 7, 4 2)10, 9, 13 They do not form a triangle They do form a triangle Acute

11. FIND THE ERROR: Maria and Colin are determining whether 5-12- 13 is a Pythagorean triple. Who is correct? Explain your reason? Maria is correct because Colin does not have the longest side as c