8-1

The Pythagorean Theorem and Its

Converse

Learning Goal

To use the Pythagorean Theorem and its converse.

Pythagorean Theorem

a2 + b2 = c2

Pythagorean Theorem

a2 + b2 = c2

The right angle touches the a and b.

Pythagorean Theorem:

a2 + b2 = 2

a

b

c

c

Pythagorean Theorem:

a2 + b2 = 2

3

x

5

c

Pythagorean Theorem:

32 + x2 = 2

3

x

5

c

Pythagorean Triples and Their Multiples

3, 4, 5

5, 12, 13

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

Which number goes in the c spot?

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

Which number goes in the c spot?Why?

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

92 + 122 = 162

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

92 + 122 = 162

81 + 144 = 256

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

92 + 122 = 162

81 + 144 = 256225 = 256

ExampleIs a triangle with side lengths 9,

12 and 16 a right triangle?

a2 + b2 = c2

92 + 122 = 162

81 + 144 = 256225 = 256

No

When you plug the 3 sides of a triangle into the Pythagorean

theorem, if the c2 is larger then it is an obtuse triangle. If it is smaller then it is an acute

triangle.

Example

a2 + b2 = c2

92 + 122 = 162

81 + 144 = 256225 = 256

Is this triangle Acute or Obtuse?

Example

a2 + b2 = c2

92 + 122 = 162

81 + 144 = 256225 = 256

Obtuse

Turn to page 495.

2, 3, 13

8-10, 19-30, 33, 36-38

5 Points: 100% Complete 4 Points: 80% Complete 3 Points: 60% Complete 2 Points: 40% Complete

1 Point: 20% Complete