In this chapter, we will start with a review of ratios and proportions. Second, we will introduce the concept of similarity and apply it to polygons, quadrilaterals and triangles. Then, we will extend proportionality to parallel lines and dilations. Finally, we conclude with an extension about fractals.
This chapter is all about proportional relationships. It begins by introducing the concept of ratio and proportion and detailing properties of proportions. It then takes these arithmetic and algebraic relationships and connects them to the geometric relationships of similar polygons. Applications of similar polygons and scale factors are covered. The AA, SSS, and SAS methods of determining similar triangles are presented and the Triangle Proportionality Theorem is explored. The chapter wraps up with the proportional relationships formed when parallel lines are cut by a transversal, similarity and dilated figures, and self-similarity.