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the rules always apply
In geometry, the rules are the rules
In geometry there’s no “i before e except after c” stuff. The rules
are the rules. Everything in your Geometry Toolbox applies
whether you think, draw, touch, look, play, or test your way to an
118 Chapter 3
answer.
1
3
2
4
Use your BRAIN
Use the REAL
WORLD
Use a PENCIL
and PAPER
Use a COMPUTER
MODEL
Your GEOMETRY TOOLBOX
works with ALL of these methods.
So no matter which of
these methods I use, I’ll
get the same answers?
Yes, you’ll get the same results however
you approach it.
Geometry is nice like that! For practical reasons, we’ll be
using your brain and a pencil and paper for this chapter,
but if you want to make use of the other methods as well
then that’s cool, too.
the pythagorean theorem
You’ve already worked out that you can build a ramp from Kwik-klik parts, using lengths 10, 8, and 6.
Which two rules from your Geometry Toolbox can help you quickly find some other lengths that
would also work?
Angles in a f
our-sided
shap
e add up t
o 360º.
If tw
o angles
add up t
o
90º, they are
complementary
Simil
ar s
hapes have
the same angles.
Simil
ar shapes hav
e the same
ratios bet
ween lengths of sides.
1
2
2
2
4
4
Angles in a
tr
iangle add up
t
o 180º.
V
ertica
lly
opp
osi
te angles
are equal.
10
6
8
you are here 4 119
use similarity
120 Chapter 3
You’ve already worked out that you can build a ramp from Kwik-klik parts, using lengths 10, 8, and 6.
Which two rules from your Geometry Toolbox can help you quickly find some other lengths that
would also work?
Simil
ar s
hap
es
hav
e the same
6
Angles in a f
our-sided
shap
e add up t
o 360º.
10
8
Angles in a
tr
iangle add up
t
o 180º.
Simil
ar s
hap
es hav
e
the same ratios
bet
w
een the lengths
of their sides, so
if w
e choose lengths
with the same ra
tios
as 6:8:10, then they’ll
definitely build
s
traight ramps.
angles, so an
y
ramp SIMILA
R
t
o the 10-8-6
ramp will a
lso have
a r
ight angle to
make the upr
ight
p
erfec
tl
y s
traight.
If tw
o angles
add up t
o
90º, they are
complementary.
Simil
ar s
hapes have
the same angles.
Simil
ar shapes hav
e the same
ratios bet
ween lengths of sides.
1
2
2
2
4
4
V
ertica
lly
opp
osi
te angles
are equal.

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