Head First 2D Geometry

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similarity and congruence

Ratios can be more useful than sizes

A ratio captures the proportions of a shape, and

then by using a different factor, we can create a

similar shape of any size.

The notes the drummer made on the diagram tell you three

ratios—what are they? Draw sketches if it helps you figure it out.

This is an important step.

This bit is easy—it’s just

multiplication or division.

By using a different factor,

here we can make the design fit

different sizes of gadgets.

This is what you

need to etch with.

All the arrows are the same.

The square part is half the

length of the arrow head part.

Triangle sides are the same.

The darker set of arrows are

3/4 size.

Factor to multiply

EVERY length by

5

12

3

Diagram with

correct ratios

Diagram with

correct lengths

94 Chapter 2

sharpen solution

The notes the drummer made on the diagram tell you three

ratios—what are they? Draw sketches if it helps you figure it out.

Q:

How come 1:1 is a ratio? Isn’t that a bit pointless?

A: It does sound a bit weird, doesn’t it? 1:1 is a way of

indicating that it’s exactly the same size as the original. If you

didn’t put the 1:1 in there, then someone reading your work or

diagram might wonder whether you’d forgotten to put a ratio in for

that item. 1:1 indicates clearly that it’s the same size. ...