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A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

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Page 1: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

a

b

c

222 cba

Page 2: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

This is a right triangle:

Page 3: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

We call it a right triangle because it contains a right angle.

Page 4: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The measure of a right angle is 90o

90o

Page 5: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The little square

90o

in theangle tells you it is aright angle.

Page 6: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.

Page 7: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Pythagorus realized that if you have a right triangle,

3

4

5

Page 8: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

and you square the lengths of the two sides that make up the right angle,

24233

4

5

Page 9: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

and add them together,

3

4

5

2423 22 43

Page 10: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

22 43

you get the same number you would get by squaring the other side.

222 543 3

4

5

Page 11: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Is that correct?

222 543 ?

25169 ?

Page 12: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

It is. And it is true for any right triangle.

8

6

10222 1086

1006436

Page 13: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The two sides which come together in a right angle are called

Page 14: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The two sides which come together in a right angle are called

Page 15: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The two sides which come together in a right angle are called

Page 16: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The lengths of the legs are usually called a and b.

a

b

Page 17: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The side across from the right angle

a

b

is called the

Page 18: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

And the length of the hypotenuse

is usually labeled c.

a

b

c

Page 19: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The relationship Pythagorus discovered is now called The Pythagorean Theorem:

a

b

c

Page 20: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,

a

b

c

Page 21: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

then

a

b

c

.222 cba

Page 22: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

You can use The Pythagorean Theorem to solve many kinds of problems.

Suppose you drive directly west for 48 miles,

48

Page 23: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Then turn south and drive for 36 miles.

48

36

Page 24: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

How far are you from where you started?

48

36?

Page 25: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

482

Using The Pythagorean Theorem,

48

36c

362+ = c2

Page 26: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Why? Can you see that we have a right triangle?

48

36c

482 362+ = c2

Page 27: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Which side is the hypotenuse? Which sides are the legs?

48

36c

482 362+ = c2

Page 28: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

22 3648

Then all we need to do is calculate:

12962304

3600 2c

Page 29: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

And you end up 60 miles from where you started.

48

3660

So, since c2 is 3600, c is 60.So, since c2 is 3600, c is

Page 30: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Find the length of a diagonal of the rectangle:

15"

8"?

Page 31: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Find the length of a diagonal of the rectangle:

15"

8"?

b = 8

a = 15

c

Page 32: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

222 cba 222 815 c 264225 c 2892 c 17c

b = 8

a = 15

c

Page 33: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Find the length of a diagonal of the rectangle:

15"

8"17

Page 34: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

Practice using The Pythagorean Theorem to solve these right triangles:

Page 35: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

5

12

c = 13

Page 36: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

10

b

26

Page 37: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

10

b

26

= 24

(a)

(c)

222 cba 222 2610 b

676100 2 b1006762 b

5762 b24b

Page 38: A b c. This is a right triangle: We call it a right triangle because it contains a right angle.

12

b

15

= 9


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