Sec' 87 Pythagorean Theorem

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Sec. 8-7Pythagorean Theorem

• Objective
• 1) To use the Pythagorean Thm.

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The Pythagorean Theorem is one of the most famous
theorems in mathematics. The relationship it
describes has been known for thousands of years.
Pythagoras (580-500 B.C.) He was a Greek
philosopher responsible for important
developments in mathematics, astronomy and the
theory of music.
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President Garfield may have been joking when he
stated about his proof that, "we think it
something on which the members of both houses
can unite without distinction of the party." A
nice feature of mathematical proofs is that they
are not subject to political opinion.
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PROVING THE PYTHAGOREAN THEOREM
THEOREM 8-1 Pythagorean Theorem
In a right triangle, the square of the length of
the hypotenuse is equal to the sum of the squares
of the lengths of the legs.
c 2 a 2 b 2
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Pythagorean Theorem
Only works for rt. ?s
a2 b2 c2
Hyp
Legs
Hypotenuse. Longest side of a rt. ?
c
a
b
Legs
Sides that form the right ?
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Example 1 Find the missing side of the ?.
a2 b2 c2 212 202 x2 441 400 x2 841
x2 v841 vx2 29 x
x
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Converse of the Pythagorean Theorem
If c is the measure of the longest side of a
triangle and c2 a2 b2 ,Then the triangle is a
right triangle
c
a
Longest side of a rt. ?
b
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Example 4 Are the following ?s, rt. ??
a2 b2 c2 842 132 852 7056 169
7225 7225 7225
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YESS!
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a2 b2 c2 482 162 502 2304 256
2500 2560 ? 2500
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Nope!
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