Pythagorean theorem

1
Pythagorean theorem

• 5.3

2
Definitions

• Hypotenuse- the side opposite the right angle
  (which is the longest side)
• Legs of a right triangle- the other two sides

Hypotenuse
Leg
Leg
3
Theorem 5.4

• In a right triangle, the sum of the squares of
  the lengths of the legs is equal to the sum of
  the square of the length of the hypotenuse. (a2
  b2 c2)

C
A
B
4
Theorem 5.5

• Converse of the Pythagorean Theorem
• If the square of the length of one side is equal
  to the squares of the lengths of the other two
  sides then the triangle is right.
• Length 5
• Length 13
• Length 12 ..Is this a right triangle?

5
Example

• Brian is out hunting deer. He sees a large buck
  across the lake where he just was. He knows from
  the deer to the big pine is 75 and from he is
  25 from the big pine himself. How far is he from
  the deer assuming from the deer to the pine to
  him is 90 degrees?

6
Example

• Find the value of x. Leave the answer in simplest
  radical form.
• a2 b2 c2
• 82 b2 202
• 64 b2 400
• b2 336
• b 4v21

8
20
x
7
Homework

• P. 259 1-36, 38-50e