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Head First 2D Geometry by Dawn Griffiths, Stray

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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 Lizs 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.
youd 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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