Head First 2D Geometry

bring in the band

Liz is back with a special request

The great thing about happy customers is that they just keep

coming back. Impressed by the effort you put in to getting her

phone just right, Liz is trusting you with another great gig.

All the arr

ows ar

e the same.

The squ

are par

t is ha

lf the

length of the arr

ow head par

t.

T

ria

ngle sides ar

e the same.

The darker set of arr

ows ar

e

3/4 size.

Hey! Everyone thinks my phone

looks great. Can you do a totally

custom design on my brother’s

iPod of his band’s logo?

T

he sketch is pretty…er…sketch

y.

Drawn on the back of a fly

er by

the drummer.

An “arrow” is

one of these.

78 Chapter 2

similarity and congruence

Before you start sketching the design, what lengths and angles

do you need to find? Could you use similarity to save yourself

some time and effort?

you are here 4 79

the arrows are similar

All the arr

ows ar

e the same.

The squ

are par

t is ha

lf the

length of the arr

ow head par

t.

T

riangle sides ar

e the same.

The darker set of arr

ows ar

e

3/4 size.

Although there aren’t any length or angle markings on the diagram,

the instructions give us plenty of clues—and there’s a ton of

similarity going on here.

T

he diagram is made up of six

simil

ar arrow shap

es like this.

A tr

iangle wi

th

thr

ee sides a

ll the

same length.

A squar

e wi

th sides

ha

lf the length of

the triangle sides.

This kind of tr

iangle is known as an

equila

teral tr

iangle (the note says

the thr

ee sides are the same), and

a

ll thr

ee angles ar

e the same as w

ell.

180

o

/3 = 60

o

There ar

e thr

ee large arrows

and thr

ee sma

ller ones, 3/4

of the size of the l

arge ones.

Before you start sketching the design, which lengths and angles

do you need to find? Could you use similarity to save yourself

some time and effort?

We need to find the lengths and angles of the sides of one of the

small triangles and one of the big triangles, plus the lengths of the

sides of one of the small squares and one of the big squares.

80 Chapter 2