Head First 2D Geometry

96 Chapter 2

pick a single starting point

Ratios need to be consistent

The ratios we took from the diagram are individually

correct, but they describe different relationships between

the lengths of our lines.

On our design, we need to make sure that we reflect all

the ratios at the same time, which means we have to pick

one thing and then work everything out relative to that.

4

3

3

2

1

2

1

4

2

That decimal

looks like it could be

tricky; if we picked some

different numbers, could

we get rid of it?

4

3

1.5

While the decimal isn’t really a problem, it’s certainly

easier to work with ratios that are only whole numbers:

your brain can compare ratios like 3:4 and 7:8 in a way

that you probably can’t just figure out which is bigger

out of 2.67:5.3 and 4.56:6.2.

We need to make

all these ratios

work together.

Divide 4 by 2 to get the

correct ratio for the square.

Divide 3 by 2 to get the

correct ratio for the square.

Let’s choose this

biggest arrow to

be the thing we’re

working relative to.

1

Now we need to

include the 4:3 ratio

between the large

and small arrows.

2

We’re ready

to use ratios!

3

you are here 4 97

similarity and congruence

The ratios have turned out to be 4, 3, 2, and 1.5.

What would be the smallest set of whole numbers you could

substitute and still keep the ratios the same?

Time to get etch