The Pythagorean Theorem

1
The Pythagorean Theorem

• 11.3

2
Objectives

• Use the Pythagorean Theorem to find the length of
  a side of a right triangle.
• Use the converse of the Pythagorean Theorem to
  determine whether a triangle is a right triangle.

3
The Pythagorean Theorem

• In a right triangle, the sides that are
  adjacent to the right angle are called the legs.
  The side opposite the right angle is the
  hypotenuse.

hypotenuse
leg
leg
4
The Pythagorean Theorem

• describes the relationship between the legs and
  the hypotenuse.
• This theorem is TRUE for ANY right triangle!!

5
2

• a b c
• Example
• 3 4 5
• 9 16 25

2
2
c
a
b
2
2
2
6
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Finding the Length of the Hypotenuse

• Find the length of the hypotenuse

c ft
2
2
2
a b c
12 ft
16 ft
2
2
12 16 c
2
2
144 256 c
2
400 c

2
c 20
400
c
8
? YOUR TURN ?

• Find the hypotenuse

c ft
21 ft
20 ft
2
2
2
21 20 c
2
441 400 c
29 ft c
9
Another one!
c
9 cm
11 cm
2
2
2
a b c
c 14.2 cm
2
2
2
9 11 c
2
81 121 c
2
202 c
10
Solve a Right Triangle

• Find the length of the leg

14 cm
a cm
10 cm
2
2
2
14 a 10
2
196 a 100
2
196 100 a
2
96 a
9.8 cm a
11
? YOUR TURN ?

• Find the length of the leg

11 m
8 m
b m
2
2
2
11 8 b
2
121 64 b
2
57 b
7.5 m b
12
Thought of the day

• A bumble bee has 5 eyes