Chapter 8

# Similarity

IN THIS CHAPTER Sizing up similar figures Doing similar triangle proofs Scoping out theorems about proportionality

You know the meaning of the word similar in everyday speech. In geometry, it has a related but more technical meaning. Two figures are similar if they have exactly the same shape.

## Similar Figures

In this section, I cover the formal definition of similarity, how similar figures are named, and how they’re positioned.

### Defining similar polygons

As you see in Figure 8-1, quadrilateral WXYZ is the same shape as quadrilateral ABCD, but it’s ten times larger (though not drawn to scale). These quadrilaterals are therefore similar. Similar polygons: For two polygons to be similar, both of the following must be true:

• Corresponding angles are congruent.
• Corresponding sides are proportional. FIGURE 8-1: These quadrilaterals are similar because they’re exactly the same shape; note that their angles are congruent.

To fully understand this definition, you ...

Get Geometry Essentials For Dummies now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.