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The Pythagorean Theorem. c. a. b. This is a right triangle:. We call it a right triangle because it contains a right angle. The measure of a right angle is 90 o. 90 o. in the. The little square. angle tells you it is a. right angle. 90 o.
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The Pythagorean Theorem c a b
We call it a right triangle because it contains a right angle.
in the The little square angle tells you it is a right angle. 90o
About 2,500 years ago, a Greek mathematician named Pythagoras discovered a special relationship between the sides of right triangles.
5 3 4 Pythagoras realized that if you have a right triangle,
5 3 4 and you square the lengths of the two sides that make up the right angle,
5 3 4 and add them together,
5 3 4 you get the same number you would get by squaring the other side.
Is that correct? ? ?
10 8 6 It is. And it is true for any right triangle.
The two sides which come together in a right angle are called
The two sides which come together in a right angle are called
The two sides which come together in a right angle are called legs.
The side across from the right angle is called the hypotenuse. a b
And the length of the hypotenuse is usually labeled c. c a b
The relationship Pythagoras discovered is now called The Pythagorean Theorem: c a b
The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c, c a b
then c a b
You can use The Pythagorean Theorem to solve many kinds of problems. 48 Suppose you drive directly west for 48 miles,
Using The Pythagorean Theorem, 48 482 + 362 = c2 36 c
48 482 + 362 = c2 36 c Why? Can you see that we have a right triangle?
48 482 + 362 = c2 36 c Which side is the hypotenuse? Which sides are the legs?
And you end up 60 miles from where you started. So, since c2 is 3600, c is 48 36 60 So, since c2 is 3600, c is
15" 8" Find the length of a diagonal of the rectangle: ?
15" 8" Find the length of a diagonal of the rectangle: ? c b = 8 a = 15
c b = 8 a = 15
15" 8" Find the length of a diagonal of the rectangle: 17
Practice using The Pythagorean Theorem to solve these right triangles:
c 5 12 = 13
b 10 26
b 10 26 = 24 (a) (c)
12 b 15 = 9