Pythagorean Theorem As posted by: oints/math/pythagorean.html.
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Transcript of Pythagorean Theorem As posted by: oints/math/pythagorean.html.
Pythagorean Theorem
As posted by: http://www.freeclubweb.com/powerp
oints/math/pythagorean.html
Objective- To solve problems involving the Pythagorean Theorem.
For Right Triangles Only!
leg
leg
hypotenuse - always oppositethe right angle
Objective- To solve problems involving the Pythagorean Theorem.
For Right Triangles Only!
leg
leg
hypotenusea
b
c
ba
ab
Objective- To solve problems involving the Pythagorean Theorem.
For Right Triangles Only!
hypotenusec
a
b
c2 2 2a b c
Pythagorean Theorem
Objective- To solve problems involving the Pythagorean Theorem.
For Right Triangles Only!
6
8
x
2 2 2a b c 2 2 26 8 x
236 64 x 2100 x
2100 x10 x
x 10 or 10
Solve for x.
4
7
y
2 2 2a b c Solve for y.
2 2 27 4 y 249 16 y 265 y
265 y
65 y
y 65 or 65 y 8.1
6
t15
2 2 2a b c Solve for t.
2 2 2t 6 15 2t 36 225
36 36 2t 1892t 189t 189t 13.7
Pythagorean Triples
3 4 5
6 8 10
9 12 15
12 16 20
Pythagorean Triples
3 4 5
6 8 10
9 12 15
12 16 20
5 12 13
10 24 26
15 36 39
7 24 25
14 48 50
21 72 75
915
12
To the nearest tenth of a foot, find the length of the diagonal of a rectangle with a width of 4 feet and a length of 10 feet.
4 ft.
10 ft.
2 2 2a b c 2 2 24 10 x
216 100 x 2116 x
2116 x
x 116
x
x 10.8
20 miles
A car drives 20 miles due east and then 45 milesdue south. To the nearest hundredth of a mile, how far is the car from its starting point?
45 milesx
2 2 2a b c 2 2 220 45 x
2400 2025 x 22425 x
22425 x
x 2425x 49.24
Informal Proof #1Inscribe a square within the square.
a b
a
a
a
b
b
b c
c
c
c
2c
Informal Proof #12Yellow region c
a b
a
a
a
b
b
b c
c
c
c
a
b c
2c
Informal Proof #12Yellow region c
b
a
a
a
b
b
c
c
c
a
b c
2c
Informal Proof #12Yellow region c
b
a
a
a
b
b
c
c
c
a
b c
2c
a
bc
Informal Proof #12Yellow region c
b
a
a
b
c
c
a
b c
2c
a
bc
Informal Proof #12Yellow region c
b
a
a
b
c
c
a
b c
2c
a
bc
b
ac
Informal Proof #12Yellow region c
a
b
c
a
b c
2c
a
bc
b
ac
Informal Proof #12Yellow region c
a
b
c
a
b c
2c
a
bc
b
aca
b
c
Informal Proof #12Yellow region c
a
b c
2c
a
bc
b
aca
b
c
Informal Proof #12Yellow region c
a
b c
a
bc
b
aca
b
c
Informal Proof #12Yellow region c
a
b c
a
bc
b
aca
b
c
Informal Proof #1
a
b c
2Yellow region c
a
bc
b
aca
b
c
Informal Proof #1
a
b c
a
bc
2Yellow region c
b
aca
b
c
Informal Proof #1
a
b c
a
bc
a
b
c
2Yellow region c
b
ac
Informal Proof #1
a
b c
a
bc
a
b
c
b
ac
2Yellow region c
Informal Proof #1
a
b c
a
bc
a
b
c
b
ac
2b
2a
2Yellow region c
2 2Yellow region a b
2 2 2a b c
a b
a
a
a
b
b
b c
c
c
c
2c
Informal Proof #2
a + bTotal Purple Yellow Area Area Area- =
2(a b) -1
4 ab2
=2c
2 2a 2ab b 2ab 2c
2 2 2a b c
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