Class Rules  No Cellphones or Headphones allowed during class. Failure to comply will result in phones being held for the class or the day by the principal.   No use of classroom power outlets are to be used to charge electronic devices. No eating or drinking other than water in class. You will be seated when the bell rings or you will be tardy. Trips outside of the classroom will cost you a tardy. (Unless notated by accommodations). No talking during quizzes or tests; you will receive a zero. Be respectful to each other and follow the instructions of the teacher.

7.1 – Apply the Pythagorean Theorem

(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem: If a triangle is a right triangle, then (hypotenuse)2 = (leg)2 + (leg)2 c leg hypotenuse a leg b (hypotenuse)2 = (leg)2 + (leg)2 c2 = a2 + b2

1. Find the value of x. c2 = a2 + b2 H x2 = 152 + 362 x2 = 225 + 1296 x2 = 1521 x = 39

1. Find the value of x. c2 = a2 + b2 x2 = 42 + 92 H x2 = 16 + 81 x2 = 97

1. Find the value of x. c2 = a2 + b2 x2 = 62 + 32 x2 = 36 + 9 H x2 = 45

1. Find the value of x. c2 = a2 + b2 172 = x2 + 82 289 = x2 + 64 H 225 = x2

1. Find the value of x. c2 = a2 + b2 272 = x2 + 92 729 = x2 + 81 648 = x2 H

1. Find the value of x. c2 = a2 + b2 422 = x2 + 362 H 1764 = x2 + 1296 468 = x2

2. Find the area of the isosceles triangle. c2 = a2 + b2 H H 102 = h2 + 82 100 = h2 + 64 8 8 36 = h2 8 in2

2. Find the area of the isosceles triangle. c2 = a2 + b2 H 122 = h2 + 42 144 = h2 + 16 128 = h2 4 cm2

2. Find the area of the isosceles triangle. c2 = a2 + b2 H 442 = h2 + 242 1936 = h2 + 576 24 24 1360 = h2 24 m2

7.2 – Converse of the Pythagorean

Pythagorean Theorem Converse: If c2 = a2 + b2, then the triangle is a right triangle c a b

Acute Triangle: If c2 < a2 + b2, then the triangle is acute c a b

Obtuse Triangle: If c2 > a2 + b2, then the triangle is obtuse c a b

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 a. 8, 15, 17 172 = 82 + 152 8 + 15 > 17 289 = 64 + 225 8 + 17 > 15 289 = 289 15 + 17 > 8 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

b. 3, 4, 9 3 + 4 > 9 7 > 9 Triangle: YES or NO For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! b. 3, 4, 9 3 + 4 > 9 7 > 9 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 c. 10, 11, 14 142 = 102 + 112 10 + 11 > 14 196 = 100 + 121 10 + 14 > 11 196 221 < 11 + 14 > 10 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 d. 61 = 25 + 36 5 + 6 > 7.8 61 = 61 5 + 7.8 > 6 6 + 7.8 > 5 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 e. 144 = 13 + 100 3.6 + 10 > 12 144 113 > 3.6 + 12 > 10 10 + 12 > 3.6 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 f. 4.3, 5.2, 6.1 4.3 + 5.2 > 6.1 37.21 = 18.49 + 27.04 4.3 + 6.1 > 5.2 37.21 45.53 < 5.2 + 6.1 > 4.3 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

HW Problem 7.1 #26 H H c2 = a2 + b2 c2 = a2 + b2 a 52 = a2 + 32 7.2 436-439 444-445 3, 5, 13-17 odd, 24, 26, 31, 39, 40 3-7 odd, 15-21 odd, 25 7.1 #26 Ans: H H c2 = a2 + b2 c2 = a2 + b2 a 52 = a2 + 32 x2 = 42 + 72 25 = a2 + 9 x2 = 16 + 49 16 = a2 x2 = 65 4 = a