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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