The Pythagorean Theorem c a b.

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Presentation transcript:

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 90o

The little square in the angle tells you it is a right angle. 90o

About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.

Pythagorus realized that if you have a right triangle, 3 4 5

and you square the lengths of the two sides that make up the right angle, 3 4 5

and add them together, 3 4 5

you get the same number you would get by squaring the other side. 3 4 5

Is that correct? ? ?

It is. And it is true for any right triangle. 8 6 10

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 lengths of the legs are usually called a and b.

The side across from the right angle is called the hypotenuse. a b

And the length of the hypotenuse is usually labeled c.

The relationship Pythagorus discovered is now called The Pythagorean Theorem: b

The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,

then c a b

Find the length of a diagonal of the rectangle: 15" 8" ?

Find the length of a diagonal of the rectangle: 15" 8" ? b = 8 c a = 15

b = 8 a = 15 c

Find the length of a diagonal of the rectangle: 15" 8" 17

Practice using The Pythagorean Theorem to solve these right triangles:

5 12 c = 13

10 b 26

= 24 10 b 26 (a) (c)

12 b 15 = 9

The numbers 3, 4 and 5 are said to form a Pythagorean Triple Pythagorean Triples There are cases when the lengths of the sides of a right-angled triangle have integral values Whole numbers only (No Fractions) 3 4 5 The 3, 4, 5 right-angled triangle is such a case The numbers 3, 4 and 5 are said to form a Pythagorean Triple 52 = 32 + 42

There are an infinite number of Pythagorean triples 5 12 13 There are an infinite number of Pythagorean triples Here are two more examples … 25 7 24

Summary Find the legs and hypotenuse. Square the legs (this is a and b) Add them together Square root them This is the length of the hypotenuse (this is c)