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Warm Up
• Write down objective and homework in agenda
• Lay out homework (Simplify Radicals)• Homework (Pythagorean Worksheet kuta)
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Simplify the radicals
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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
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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
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Pythagorean Theorem
• The formula for the Pythagorean Theorem is• a2 + b2 = c2
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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
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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
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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
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You Try!Calculate the missing side of a right triangle
• a2 + b2 = c2
• x = 4.9leg
hypotenuse
leg
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You Try!
• X = 5.4
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Pythagorean Triple
• A Pythagorean triple consists of three positive WHOLE NUMBER that fit into the Pythagorean Theorem
• Example: 32 + 42 = 52
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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
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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
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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
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You Try! Determine whether a triangle with the given side lengths is a right triangle
• a = 6.4, b = 12, c = 12.2
• NO!
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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
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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
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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