PYTHAGOREAN THEOREM – DAY 1

January 20th , 2010

Classroom Jobs Congratulations to:

Max - Exit Slip Captain

Aracely - Notebook Captain

Autavia -Homework Stamper #1

Susana - Homework Stamper #2

Larissa - Special Helper

It’s CST Challenge Please fill out name and top sentenceFar Below BasicBelow BasicBasicProficientAdvanced

Begin reading!

Good luck We can win!!

Good Morning

Warm-Up – homework on desk!

1.

2.

3.

Challenge:

19

8

169

18

€

3 36€

361

€

64

€

132

And the winner is….

Period 1 Period 2 Period 4 Period 50

10

20

30

40

50

60

70

80

90

100

Homework

Homework

Period 1 – 81 %!!

81%

77 %

79 %

74 %

Let’s Check our Homework

1. D

2. C

3. B

4. 96

5. 5x + 20

6. 56 – 16x

This Week’s Agenda

Tuesday – Right Triangles

Wednesday – Pythagorean Theorem

Thursday – Pythagorean Theorem

Friday – Quiz!

Agenda Warm-Up (10 minutes)

Vocabulary (10 minutes)

Pythagorean Theorem Poster (10 minutes)

Practice, Practice, Practice (25 minutes)

Exit Slip (5 minutes)

Objective

I CAN DEFINE AND APPLY THE PYTHAGOREAN THEOREM

Pythagoras Greek Mathematician

Born around 500 B.C. Over 2500 years ago

Discovered something very, very, very, very special about right triangles.

So special there is now a law named after him…

Pythagorean Theorem In any right triangle, the sum

of the squares of the two legs is equal to the square of the hypotenuse.

a2 + b2 = c2

a

b

c

Right Triangle Detectives

What did we learn?????

In order to be a right triangle, the pythagorean theorem must hold true!

a2 + b2 = c2

Is a triangle with sides of length 4, 6, 8 a right triangle?

a2 + b2 = c2

42 + 62 = 82

16 + 36 = 6452 = 64

NO! not a right triangle

4

6

8

Is a triangle with sides of length 7, 11, 14 a right triangle?

a2 + b2 = c2

72 + 112 = 142

49 + 121 = 196170 = 196

NO! not a right triangle

7

11

14

Is a triangle with sides of length 9, 12, 15 a right triangle?

a2 + b2 = c2

92 + 122 = 152

81 + 144 = 225225 = 225

YES! It is a right triangle

9

12

15

A triangle has legs measuring 6 cm and 8 cm, what is the length of the hypotenuse??

1. Draw a picture

2. Write down Pythagorean theorem

15

8

?a2 + b2 = c2

3. Substitute in what you know

152 + 82 = c2

225 + 64 = c2

289 = c2

4. Take square root!!

17 = c17 cm

€

289 = c 2

Coach Meyer

17 cm

Steps: 1. Draw a picture of triangle if needed

2. Write down the Pythagorean Theorem

3. Substitute in the two sides you know.

4. Take square root to find length of the hypotenuse

A triangle has sides measuring 5 cm and 12 cm, what is the length of the hypotenuse??

1. Draw a picture

2. Write down Pythagorean theorem

5

12

?a2 + b2 = c2

3. Substitute in what you know

52 + 122 = c2

25 + 144 = c2

169 = c2

4. Take square root

13 = c13 cm

€

169 = c 2

We do

13

A triangle has sides measuring 7 cm and 8 cm, what is the length of the hypotenuse??

1. Draw a picture

2. Write down Pythagorean theorem

7

8

?a2 + b2 = c2

3. Substitute in what you know

72 + 82 = c2

49 + 64 = c2

113 = c2

4. Take square root

€

113 = c 2

We do

€

113 = c

€

113

1. Draw a picture

2. Write down Pythagorean theorem

3

10?

a2 + b2 = c2

3. Substitute in what you know

32 + 102 = c2

9 + 100 = c2

109 = c2

4. Take square root

√109

€

109 = c 2

We do

€

109 = c

€

109

You - do Find the hypotenuses of the following

right triangles: 1. legs: 6, 8

2. legs: 9, 10

3. legs: 12, 16

4. legs: 8, 15

Hypotenuse = 10

Hypotenuse = √181

Hypotenuse = 20

Hypotenuse = 13

Finish Your poster! Add the Pythagorean Theorem in large letters

Write the formula below the theorem

Show how the Pythagorean theorem works for your triangle with sides 3, 4, 5.

If you have not, find the area of each of the 3 squares and write in the center of the square

Make your poster colorful and pretty to put up on the walls!

Exit Slip

Work quietly

Please keep your eyes on your own paper