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9.2 The Pythagorean Theorem. Did Pythagoras of Samos discover the Pythagorean theorem?. The Pythagorean Theorem. In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. The Pythagorean Theorem. - PowerPoint PPT Presentation
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9.2 The Pythagorean Theorem
Did Pythagoras of Samos discover the Pythagorean
theorem?
The Pythagorean Theorem
In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.
a
b
c
222 cba
The Pythagorean Theorem
In a Right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.
c
222 cba
7
24 25
247 22
c
c
Pythagorean Triples
If the sides of a Right triangle are integers, then the sides are known as a Pythagorean Triple
7, 24, 25
Do you know any other ?
Pythagorean Triples
If the sides of a Right triangle are integers, then the sides are known as a Pythagorean Triple
7, 24, 25
Do you know any other ?
3, 4, 5
5, 12, 13
Solve for x
A Right Triangle
x12
56
222
1256 x
Solve for x
A Right Triangle
x12
56
6
36
144180
144536
1256
2
2
2
222
x
x
x
x
x
Area and the Right Triangle
Area equals ½ altitude times base A=½ab
b and a are the same as the legs of a Right triangle.
3
4
6
432
1
A
A
2 poles are supported by 100ft cables 50 ft from the ground
How far are the poles apart?
ft100ft100 ft100
ft100
ft50 ft50
2 poles are supported by 100ft cables 50 ft from the ground
How far are the poles apart?
ft100ft100 ft100
ft100
ft50 ft50
x x
6.86350
7500
250010000
50100
2
2
222
x
x
x
x
2 poles are supported by 100ft cables 50 ft from the ground
How far are the poles apart?
ft100ft100 ft100
ft100
ft50 ft50
x x
ft2.1736.866.86
Solve for y
Use the Right Triangle
5y
1y
222 15 yy
Solve for y
Use the Right Triangle
5y
1y
13
226
0262
262
1225
15
22
22
222
y
y
y
yyy
yyy
yy
Homework
Page 538 – 541
# 8 – 24 even,
25 - 31, 33, 34,
39, 40
• The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework. http://en.wikipedia.org/wiki/Pythagorean_theorem#Proof_using_similar_triangles
