8-6 The Pythagorean Theorem Pythagorus (say "pie-thag-or-us") of Samos was a Greek philosopher who...
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8-6 The Pythagorean Theorem Pythagorus (say "pie-thag-or-us") of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. He made important developments in mathematics, astronomy, and the theory of music. Pythagoras spent much of his life studying mathematics and formed a special school where members followed strict rules, such as never eating meat. Pythagoras believed that everything in the world could be explained by numbers and his school worked hard to try to learn enough about
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Transcript of 8-6 The Pythagorean Theorem Pythagorus (say "pie-thag-or-us") of Samos was a Greek philosopher who...
8-6 The Pythagorean Theorem
Pythagorus (say "pie-thag-or-us") of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. He made important developments in mathematics, astronomy, and the theory of music.Pythagoras spent much of his life studying mathematics and formed a special school where members followed strict rules, such as never eating meat. Pythagoras believed that everything in the world could be explained by numbers and his school worked hard to try to learn enough about numbers to be able to understand the universe.
How we use the How we use the Pythagorean theoremPythagorean theorem To find the missing side length in To find the missing side length in
a right triangle when you know a right triangle when you know two side lengthstwo side lengths
To determine if three given side To determine if three given side lengths form a right trianglelengths form a right triangle
Only works with right TrianglesOnly works with right Triangles
leg
leg
hypotenuse
c2 = a2 + b2
Longest side
Right angle
ca
b
c2 = a2 + b2
c2=a2+b2
15 in
8 in
x
c2=a2+b2
x2=152+82
X2=225+64
X2=289
X = 17
Find a missing side length
4 cm
4 cm
y
c2=a2+b2
y2=42+42
y2=16+16
y2=32
y = 5.66
Find a missing side length
25 m20 m
c2=a2+b2
252=202+x2
625=400+x2
625-400 =x2
225 =x2
15 = x x
Find a missing side length
12 m
15 m
y
c2=a2+b2
152 = 122+x2
225 = 144+x2
225 - 144 =x2
81 =x2
9 = x
Find a missing side length
Determine if the three given sides form a right Triangle
6, 8, 10
C2 = a2 + b2
102 = 62 + 82
100 = 36 + 64
100 = 100
Yes it is a Right Triangle
Determine if the three given sides form a right Triangle
4, 8, 7
C2 = a2 + b2
82 = 72 +42
64 = 49 + 16
64 = 65
No it is NOT a right Triangle
