t

oday’s sma

ller gadgets.

the phone’s size is important

It’s a problem of scale…

The design Liz picked was originally created in 2007, when

phones were a lot bigger than the one Liz has today. In fact,

the design is twice as big as the space available on the back of

Liz’s phone for etching!

2007 phone

T

oday’s phone

myP

od-designs-(c) 2007

T

his design needs t

o

be updated t

o fi

t on

…but how big a problem is it?

Q:

How come there weren’t any units on the drawing? If

they’d put units we could have seen whether it fit before we

started etching.

A:You’re right, we could have. In this case, though, the lengths

on the diagram wouldn’t be normal measures like millimeters or

inches, but a special measure used by the etching machine.

Q:

But shouldn’t the drawing still have a scale? Wouldn’t

we be best to add one now?

A:For now we can just adjust the lengths we’ve got to work

with—we can safely assume that whatever units the etcher uses,

they aren’t going to change before we etch again. But in the next

chapter we’re going to look at using scales in a lot more detail.

70 Chapter 2

similarity and congruence

Pool Puzzle

Your job is to take steps from the pool

that you think will help you make

the design fit on Liz’s new phone,

and use them to complete your

to-do list. (You don’t need to use

them all.)

1) Create a clean copy of the diagram with no numbers on it.

2)

3)

Note: each thing from

the pool can only be

used once!

Copy the lengths from the old

diagram, but divide them by two.

Ask Liz to pick a new design.

Do some really hard geometry

Start calculating the angles over again.

to work out the new lengths.

Trash the diagram

Copy the lengths from the old

diagram, but multiply them by two.

Copy all the angles that

and go home.

you’d already worked out.

you are here 4 71

And a

ll the lengths

change by the same

F

ACT

OR.

W

hen y

ou s

hrink

the angles don’t

something ev

enl

y,

change.

A f

ac

t

or is a common multipli

er—

like if w

e doubled y

our pay and

a

lso doubled y

our hour

s, w

e w

ould

hav

e incr

eased both by a fac

t

or

of 2.

factoring for size

Pool Puzzle Solution

Your job is to take from the pool the

steps you think will help you make

the design fit on Katie’s new phone,

and use them to complete your

to-do list.

1) Create a clean copy of the diagram with no numbers on it.

2)

Copy all the angles that you’d already worked out.

3) Copy the lengths from the old diagram, but divide them by two.

Ask Liz to pick a new design.

Start calculating the angles over again.

Do some really hard geometry

to work out the new lengths.

Trash the diagram

Copy the lengths from the old

and go home.

diagram, but multiply them by two.

72 Chapter 2

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