Warm Up Write down objective and homework in

Warm Up • Write down objective and homework in agenda • Lay out homework (Simplify Radicals) • Homework (Pythagorean Worksheet kuta)

Simplify the radicals

Vocabulary hypotenuse longest side of a right triangle, opposite the right angle legs the two sides of a right triangle that make up the right angle Pythagorean Theorem angle that measures 90 degrees theorem that states in a right triangle the length of the hypotenuse (c) squared is equal to the sum of the squares of the lengths of the legs a 2 + b 2 = c 2 Pythagorean Triple three positive integers that make up the lengths of the sides of a right triangle

Pythagorean Theorem Deals with the relationship between the side lengths in a right triangle • Sides A and B are called the…. – Legs! • Side C is called the…. – Hypotenuse • Side C is always the …. – Longest side! • Side C is always across the right angle

Pythagorean Theorem • The formula for the Pythagorean Theorem is • a 2 + b 2 = c 2

Example 1 Calculate the missing side of a right triangle hypotenuse leg • • • a 2 + b 2 = c 2 182 + 152 = x 2 324 + 225 = x 2 549 = x 2 x = 23. 4 ft

Example 2 Calculate the missing side of a right triangle leg hypotenuse • • • a 2 + b 2 = c 2 82 + x 2 = 122 64 + x 2 = 144 - 64 -64 x 2 = 80 x = 8. 9 cm

Example 3 • • • a 2 + b 2 = c 2 3. 62 + x 2 = 7. 42 12. 96 + x 2 = 54. 76 - 12. 96 -12. 96 x 2 = 41. 8 x = 64. 5

You Try! Calculate the missing side of a right triangle leg • a 2 + b 2 = c 2 • x = 4. 9 leg hypotenuse

You Try! • X = 5. 4

Pythagorean Triple • A Pythagorean triple consists of three positive WHOLE NUMBER that fit into the Pythagorean Theorem • Example: 32 + 42 = 52

Example 1 Determine whether a triangle with the given side lengths is a right triangle • 7 in, 24 in, 25 in • (always place numbers in the order listed into the formula) • 72 + 242 = 252 • 49 + 576 = 625 • 625 = 625 • Yes, it is a right triangle

Example 2 Determine whether a triangle with the given side lengths is a right triangle • 6 m, 7 m, Ѵ 85 m • (always place numbers in the order listed into the formula) • 62 + 72 = Ѵ 852 • 36 + 49 = Ѵ 852 • 85=85 • Yes, it is a right triangle

You Try! Determine whether a triangle with the given side lengths is a right triangle • 8 cm, 10 cm, 12 cm • No, it is NOT a right triangle! • 82 + 102 = 12. 8

You Try! Determine whether a triangle with the given side lengths is a right triangle • a = 6. 4, b = 12, c = 12. 2 • NO!

Find the circumference and area of the circle below: • • • First calculate r. Side MP = 12 in. 52 + 122 = r 2 r = 13 in. C = 2πr C = 2(3. 14)(13) C = 81. 6 in. A = πr 2 A = (3. 14)(132) A = 530. 7 in 2

Practice! • http: //www. quia. com/rr/624643. html • http: //www. ixl. com/math/grade 8/pythagorean-theorem-find-the-missing-leglength • http: //www. ixl. com/math/grade-8/converseof-the-pythagorean-theorem-is-it-a-righttriangle

Extra Resources • http: //www. cpm. org/pdfs/skill. Builders/GC/GC _Extra_Practice_Section 5. pdf • http: //www. mathsisfun. com/pythagoras. html • http: //www. purplemath. com/modules/pytha gthm. htm • http: //www. mathscore. com/math/practice/P ythagorean%20 Theorem/ • http: //www. quia. com/rr/541969. html