pythagorean theorem day 1
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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