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Head First 2D Geometry by Dawn Griffiths, Stray

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Author’s note: In Br
i
tis
h
Englis
h, i
t’s known as
Pythagoras’ T
heorem.
the pythagorean theorem
The Pythagorean Theorem: a
2
+ b
2
= c
2
This pattern is known as The Pythagorean Theorem. Using it you
can find out whether the corner opposite the longest side of a triangle is
acute, obtuse, or a right angle. In words, the theorem is usually written:
The sum of the squares of the legs of a right
triangle is equal to the square of the hypotenuse.
T
he “h
yp
otenuse” is the
longest side.
T
hese other t
w
o
sides are ca
lled “legs.”
T
his is how it’s wri
tten as a f
ormul
a.
a
2
+ b
2
= c
2
a
c
b
a
a
2
+ b
2
> c
2
c
a
a
2
+ b
2
< c
2
For an OBTUSE triangle:
For an ACUTE triangle:
c
b
b
you are here 4 131
So we don’t need to know them
all in advance? We can check jumps
as we go? Perfect—because I’ve
just told everybody we’re setting up a
competition on one of our courses!
skate ramp magnets
Skate Ramp Magnets
Sam’s sketched out a rough design for the competition course. She wants
three different sets of ramps for the skaters to demo their skills on—one
with a gap to jump and two with joining rails to slide on.
Using the Pythagorean Theorem and the construction kit magnets, work
out where each part needs to go to complete the course design. Use each
part exactly once.
6
5
Less than 11 wide
More than 11 wide
8
Less than 11 wide
More than 11 wide
132 Chapter 3
3
6
7
8
10
4 5
the pythagorean theorem
7
I know how high I’d like them to be,
and it’d be cool if all the ramps on the
left were less than 11 wide, and all the
ramps on the right were more than 11
wide. Just use whatever you’ve got left
over for the slide rails.
3
Less than 11 wide
More than 11 wide
12
14
15
24
25
you are here 4 133
13
17
S
o
Q
t
e
u
r
r
s
t
u
g
w
gli
e
n
g
m
to g
?
et
h
s
t
a
k
rt
u
ed
?
t
F
ee
N
li
n
g
Dv
h
l
ed
C ec
o t h
e
o
u
m
b
e
i
o
n
s
o
n p
age
14
1
to get
o
f
f
t
h
e
blocks....
If y
ou don’t know y
our
square number
s make
y
our
self a list when y
ou
s
tart the ques
tion.
14 was left over
after making a
ll
the tr
iangles.
skate ramp magnets solution
Skate Ramp Magnets Solution
Sam’s sketched out a rough design for the competition course. She wants
three different sets of ramps for the skaters to demo their skills on—one
with a gap to jump and two with joining rails to slide on.
Using the Pythagorean Theorem and the construction kit magnets, work
out where each part needs to go to complete the course design. Use each
part exactly once.
Solving this problem is mostly a matter of trial and error—checking to
see where you can find lengths which fit the Pythagorean Theorem:
Longest side squared = sum of other two sides squared.
6
2
+ 8
2
= 36 + 64 = 100
10
2
= 100
5
2
+ 12
2
= 25 + 144 = 169
13
2
= 169
10
13
6
5
8
14
12
17
10
8
8
6
2
+ 8
2
= 36 + 64 = 100
10
2
= 100
8
2
+ 15
2
= 64 + 225 = 289
17
2
= 289
6
15
3
6
7
8
10
4 5
134 Chapter 3

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