February 13, 2013
5.7 The Pythagorean Theorem
c
a
b
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February 13, 2013
Proof
d
c
a
e
b
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Pythagorean Triple:
set of positive integers a, b, and c, that satisfy a2+b2=c2
Ex.
3, 4, 5
5, 12, 13
8, 15, 17
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Examples. Find x.
1.
x
7
24
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2.
12
x
6√5
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x
x-2
4
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Randy is building a rectangular picture frame. He wants
the ratio of the length to the width to be 3:1 and the
diagonal to be 12 cm. How wide should the frame be?
Round to the nearest tenth of a centimeter.
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a
c
b
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Converse of the Pythagorean Theorem
If
c2 = a2 + b2
then right triangle
also if
c2 < a2 + b2
then an acute triangle
c2 > a2 + b2
then an obtuse triangle
February 13, 2013
Acute, Right, or Obtuse?
1.
7, 10, 13.4
3. 12.3, 16.4, 20.5
2. 6, 6
5 , 12
4. 13, 5, 7
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3. Find the area.
8
8
10