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
Pythagorean theorem


To find the missing side length in a
right triangle when you know two side
lengths
To determine if three given side
lengths form a right triangle
Only works with right Triangles
c2 = a2 + b2
hypotenuse
leg
Longest side
Right angle
leg
c2 = a2 + b2
c
a
b
2
2
2
c =a +b
Find a missing side length
c2=a2+b2
x2=152+82
X2=225+64
x
15 in
X2=289
X = 17
8 in
Find a missing side length
c2=a2+b2
y2=42+42
4 cm
4 cm
y2=16+16
y2=32
y = 5.66
y
Find a missing side length
c2=a2+b2
252=202+x2
625=400+x2
25 m
20 m
625-400 =x2
225 =x2
15 = x
x
Find a missing side length
c2=a2+b2
152 = 122+x2
225 = 144+x2
225 - 144 =x2
81 =x2
9=x
12 m
y
15 m
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