Head First 2D Geometry

testing with accurate construction

You can use accurate construction to

test ramp designs on paper

Accurate construction is different from making a sketch.

A s

har

p p

encil

A c

entimeter ruler,

ideall

y one wi

th

millimeter markings

as w

ell

A sca

le

You’ll need:

Scale: 1cm

=

1 Kwik-klik unit

Y

our eyes

Gr

id pap

er in

incr

ements of

c

entimeter

s

ACCURATE CONSTRUCTION

108 Chapter 3

the pythagorean theorem

Hello? Didn’t you spend

chapters 1 & 2 going on

about how we couldn’t trust

a drawing, couldn’t just

measure it, blah, blah, blah?

True. But making an accurate

construction is different.

How is making your own accurate drawing different from just

measuring a sketch or diagram you’re given? Write out your

answer in words below.

you are here 4 109

your drawing is accurate

110 Chapter 3

How is making your own accurate drawing different from just

measuring a sketch or diagram you’re given?

Right, so if we

know we’ve kept to the same

scale—like using a line exactly

3cm long for a size 3 Kwik-klik

piece—we can use drawing to kind

of simulate the ramp?

Yup. If you can’t draw it with a right

angle, then you can’t build it with a

right angle, either!

Centimeter grid paper has horizontal and vertical

lines which are perfectly perpendicular—making

it extra useful for drawing shapes with right angles

like our ramps need to be. Just try it out.…

If you’re drawing the diagram yourself you can keep it in proportion, and you can get the

angles right, too. You can use a set square or a protractor, or gridded paper, to make

sure lines that are supposed to be perpendicular are drawn at right angles.

If you draw a line 3cm and another line 6cm—measured with a good ruler—you know for

sure that the first line you drew is half the length of the other.

When you’re given a sketch you don’t know whether the person who drew it used a ruler

and protractor to make the drawing accurate, or just did it roughly.

Y

our answ

er might be w

orded

dif

ferentl

y—tha

t’s OK, it’s

the thought tha

t counts....

the pythagorean theorem

T

he lines on this pap

er ar

e

p

er

p

endicul

ar, so w

e know

tha

t this is a right angle.

T

his line represents the base

of y

our ramp—so the length

is exac

tl

y 12 cm.

As close as y

ou can measur

e

wi

th a millimeter ruler,

don’t w

orry about getting a

magnifi

er out!

If one of these dashed lines is exactly

13cm long, then it’ll meet the vertical

line at the height you need to use.

Use accurate construction to find what length the vertical piece

needs to be in order for the ramp to have a perpendicular upright.

Using a scale of 1cm to 1 Kwik-klik unit (so a piece of length 2

would be drawn as 2cm), use your ruler to find the part that fits.

and ruler

you are here 4 111

sharpen solution

Use accurate construction to find what length the vertical pole

needs to be in order for the ramp to have a perpendicular upright.

Using a scale of 1cm to 1 Kwik-klik unit (so a part of length 2

would be drawn as 2cm), use your ruler to find the part that fits.

and ruler solution

5cm

T

his line is exac

tl

y 13cm long.

The size 5 upright gives us a perfect vertical

The parts with lengths 12, 13, and 5 make a perfect ramp with

a right angle between the horizontal and vertical parts.

Of course what we just drew was a scaled version of our final

ramp—nobody wants a skate ramp 5cm high, but a ramp that’s

5 kwik-klik units high is plenty big enough.

If one of these dashed lines is exactly

13cm long, then it’ll meet the vertical

line at the height you need to use.

112 Chapter 3