Chapter 8

Similarity

IN THIS CHAPTER

Bullet Sizing up similar figures

Bullet Doing similar triangle proofs

Bullet 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.

Remember Similar polygons: For two polygons to be similar, both of the following must be true:

  • Corresponding angles are congruent.
  • Corresponding sides are proportional.
Geometry of two quadrilaterals ABCD and PQRS that are similar with congruent angles.

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 ...

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