8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
8.1 The Pythagorean Theorem a
a
c
c
b
b
Goal: Apply the Pythagorean Theorem and its inverse to solve right triangles. Feb 20­5:09 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Mar 2­12:50 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Warm­up
Feb 21­10:00 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
What is the Pythagorean Theorem?
equation
a
a
c
b
c
variables
hypotenuse, legs
b
what kind of triangles does it deal with
what does it allow us to find
Feb 20­5:27 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Now it's your turn to prove the Pythagorean theorem!!!!
Feb 20­5:30 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Pythagorean Theorem Cont.
Which of the following are Pythagorean triples?
(there is more than one)
a. 3, 4, 5
b. 7, 11, 13 c. 8, 15, 17
d. 9, 12, 15
Feb 21­9:59 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Practice
Find the value of x.
x
Feb 21­11:04 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Converse of the Pythagorean Theorem
If the square of the large side of the triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Feb 21­11:14 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Is the triangle a right triangle?
a.
b. A triangle with side lengths 16,
48, and 50.
Feb 21­11:20 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Homework
Pg. 420
# 1 ­ 9 odd, 18, 19, 20,
27, 29
Feb 21­11:24 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
8.2: Special Right Triangles
(First half)
Goal: Apply the properties of 45o­45o­90o triangles
to find missing side lengths.
Feb 21­11:57 AM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Mar 2­12:56 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
It's a SPECIAL right triangle
Example
1
√2
Non­example
5
2
√2
3√2
2√2
1
5
6
√2
3√2
√2
√2
√2
5
1
5
1
√2
5√2
6
3
3
Feb 21­12:05 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
What did we notice about the sides of the triangles?
Seeing this is an isosceles triangle we can use the Pythagorean theorem to figure out the length of the hypotenuse. y
x
x
Feb 21­12:32 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Practice: Find the value of each variable
5√ 3
y
Feb 21­12:38 PM
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8.1 Pythagorean Thrm and Start of 8.2 Special Right Triangles
March 02, 2010
Homework (Part 2)
Pg. 428
# 1 ­ 6, 8, 22
Feb 21­1:00 PM
16