Warm Up

• Write down objective and homework in agenda

• Lay out homework (Simplify Radicals)• Homework (Pythagorean Worksheet kuta)

Simplify the radicals

Vocabularyhypotenuse longest side of a right triangle, opposite the right

angle

legs the two sides of a right triangle that make up the right angle

right angle angle that measures 90 degreesPythagorean Theorem

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 a2 + b2 = c2

Pythagorean Triple three positive integers that make up the lengths of the sides of a right triangle

Pythagorean TheoremDeals 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• a2 + b2 = c2

Example 1Calculate the missing side of a right triangle

• a2 + b2 = c2

• 182 + 152 = x2

• 324 + 225 = x2

• 549 = x2

• x = 23.4 ft

leg

leg

hypotenuse

Example 2Calculate the missing side of a right triangle

• a2 + b2 = c2

• 82 + x2 = 122

• 64 + x2 = 144• - 64 -64• x2 = 80• x = 8.9 cm

leg

hypotenuse

leg

Example 3

• a2 + b2 = c2

• 3.62 + x2 = 7.42

• 12.96 + x2 = 54.76• - 12.96 -12.96• x2 = 41.8• x = 64.5

You Try!Calculate the missing side of a right triangle

• a2 + b2 = c2

• x = 4.9leg

hypotenuse

leg

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, Ѵ85m• (always place numbers in the order listed into

the formula)• 62 + 72 = Ѵ852 • 36 + 49 = Ѵ852

• 85 = Ѵ852

• 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 = r2

• r = 13 in.• C = 2πr• C = 2(3.14)(13) • C = 81.6 in. • A = πr2

• A = (3.14)(132)• A = 530.7 in2

Practice!

• http://www.quia.com/rr/624643.html

• http://www.ixl.com/math/grade-8/pythagorean-theorem-find-the-missing-leg-length

• http://www.ixl.com/math/grade-8/converse-of-the-pythagorean-theorem-is-it-a-right-triangle

Extra Resources

• http://www.cpm.org/pdfs/skillBuilders/GC/GC_Extra_Practice_Section5.pdf

• http://www.mathsisfun.com/pythagoras.html• http://www.purplemath.com/modules/pythag

thm.htm• http://www.mathscore.com/math/practice/Py

thagorean%20Theorem/

• http://www.quia.com/rr/541969.html