a b c 2 2 2 c b a
A b c. Use the Pythagorean Theorem and its converse to solve problems. Objectives.
Dec 26, 2015
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a
b
c
222 cba
Use the Pythagorean Theorem and its converse to solve problems.
Objectives
Pythagoras was a Greek philosopher and religious leader.He was responsible for many important developments in math,
astronomy, and
music.
Pythagoras (~560-480 B.C.)
His students formed a secret society called the Pythagoreans.
As well as studying maths, they were a political and religious organisation.
Members could be identified by a five pointed star they wore on their clothes.
The Secret Brotherhood
They had to follow some unusual rules. They were not allowed to wear wool, drink wine or pick up anything they had dropped! Eating beans was also strictly forbidden!
The Secret Brotherhood
Pythagoras realized that if you have a right triangle,
3
4
5
and you square the lengths of the two smaller sides,
24233
4
5
and add them together,
3
4
5
2423 22 43
22 43
you get the same number you would get by squaring the larger side.
222 543 3
4
5
Is that correct?
222 543 ?
25169 ?
It is, and it is true for any right triangle.
8
6
10222 1086
1006436
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
The lengths of the legs are usually called a and b.
a
b
The side across from the right angle
a
b
is called the
And the length of the hypotenuse
is usually labeled c.
a
b
c
The relationship Pythagoras discovered is now called The Pythagorean Theorem:
a
b
c
The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,
a
b
c
then
a
b
c
.222 cba
The Pythagorean Theorem is probably the most famous relationship in mathematics.
a2 + b2 = c2
Let’s practice !!!
Using the Pythagorean Theorem
Find the value of x. Give your answer in simplest radical form.
a2 + b2 = c2 Pythagorean Theorem
22 + 62 = x2 Substitute 2 for a, 6 for b, and x for c.
40 = x2 Simplify.
Find the positive square root.
Simplify the radical.
Check It Out! Example 1a
Find the value of x. Give your answer in simplest radical form.
a2 + b2 = c2 Pythagorean Theorem
42 + 82 = x2 Substitute 4 for a, 8 for b, and x for c.
80 = x2 Simplify.
Find the positive square root.
Simplify the radical.
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