Discovering

Geometry

Chapter 9

Lesson 1: 9.1, 9.2, 9.5

Lesson 2: 9.3

Lesson 3: 9.4

WARM-UP

Draw a scalene right triangle

Label the parts you remember.

Measure the sides.

SECTIONS 9-1, 9-2 AND 9-5:

THE PYTHAGOREAN THEOREM AND DISTANCE

In these sections we will answer…

Why is it so important to be right?

What is the Pythagorean Theorem?

How can I tell a right triangle from a wrong one?

How can I use Pythagorean Theorem to solve real life

problems?

How can I determine distance on the coordinate

plane?

PYTHAGOREAN THEOREM

a2 + b2 = c2

where a and b are legs and

c is the hypotenuse or longest

side

***Pythagorean Theorem only

works on RIGHT TRIANGLES!

Pythagorean Practice

Solve the following using the

Pythagorean Theorem:

1. Find c if a = 3 and b = 4.

2. Find c if a = 12 and b= 5.

3. Find b if a = 4 and c = 8

4. Find a if b = 6 and c = 9.

5. Find b if a = 15 and c = 18.

A

b

a

c

C B

2 2 2a b c

ANSWERS:

1. c = 5

2. c = 13

3. c = 6.9 or 4

4. a = 6.7 or 3

5. b = 9.9 or 3

3

5

11

How can you tell if a triangle is right using

the Pythagorean Theorem?

Right: c2 = a2 + b2

Obtuse: c2 > a2 + b2

Acute: c2 < a2 + b2

ARE THESE RIGHT TRIANGLES? IF NOT, IS

IT OBTUSE OR ACUTE?

USING THE PYTHAGOREAN THEOREM

TO SOLVE PROBLEMS:

USING THE PYTHAGOREAN THEOREM

TO SOLVE PROBLEMS:

A rectangular garden 6 meters wide has a diagonal

measuring 10 meters. Find the perimeter of the garden.

USING THE PYTHAGOREAN THEOREM

TO SOLVE PROBLEMS:

How high up on the wall will a 20-foot ladder touch if

the foot of the ladder is placed 5 feet from the wall?

USING THE PYTHAGOREAN THEOREM TO FIND

DISTANCE ON THE COORDINATE PLANE:

THE DISTANCE FORMULA:

1 1 2 2The distance between points ( , ) and ( , ) is given by

2 2 1 12 2

( ) ( )

A x y B x y

AB x x y y

FIND THE DISTANCE BETWEEN THE POINTS:

USING THE DISTANCE FORMULA TO SOLVE

PROBLEMS

Find the perimeter of ∆ABC with vertices A(2 , 4),

B(8 , 12), and C(24 , 0).

SIDE LENGTH

SIDE SLOPE DISTANCE

AB

BC

CD

DA

HOMEWORK

Worksheet 9-1, 9-2, 9-5 (front and back)