Chapter 7: Similarity
Introduction
In this chapter, we will start with a review of ratios and proportions. Second, we will introduce the concept of similarity. Two figures are similar if they have the same shape, but not the same size. We will apply similarity to polygons, quadrilaterals and triangles. Then, we will extend this concept to proportionality with parallel lines and dilations. Finally, there is an extension about selfsimilarity, or fractals, at the end of the chapter.
 7.1.
Forms of Ratios
 7.2.
Proportion Properties
 7.3.
Similar Polygons and Scale Factors
 7.4.
AA Similarity
 7.5.
Indirect Measurement
 7.6.
SSS Similarity
 7.7.
SAS Similarity
 7.8.
Triangle Proportionality
 7.9.
Parallel Lines and Transversals
 7.10.
Proportions with Angle Bisectors
 7.11.
Dilation
 7.12.
Dilation in the Coordinate Plane
 7.13.
SelfSimilarity
Chapter Summary
Summary
This chapter is all about proportional relationships. It begins by introducing the concept of ratio and proportion and detailing properties of proportions. It then focuses on 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 selfsimilarity.
Chapter Keywords
 Ratio
 Proportion
 Means
 Extremes
 CrossMultiplication Theorem
 Similar Polygons
 Scale Factor
 AA Similarity Postulate
 Indirect Measurement
 SSS Similarity Theorem
 SAS Similarity Theorem
 Triangle Proportionality Theorem
 Triangle Proportionality Theorem Converse
 Transformation
 Rigid Transformation
 Nonrigid Transformation
 Dilation
 SelfSimilar
 Fractal
Chapter Review
 Solve the following proportions.

\begin{align*}\frac{x+3}{3}=\frac{10}{2}\end{align*}
x+33=102 
\begin{align*}\frac{8}{5}=\frac{2x1}{x+3}\end{align*}
85=2x−1x+3

\begin{align*}\frac{x+3}{3}=\frac{10}{2}\end{align*}
 The extended ratio of the angle in a triangle are 5:6:7. What is the measure of each angle?
 Rewrite 15 quarts in terms of gallons.
Determine if the following pairs of polygons are similar. If it is two triangles, write why they are similar.
 Draw a dilation of \begin{align*}A(7, 2), B(4, 9),\end{align*}
A(7,2),B(4,9), and \begin{align*}C(1, 4)\end{align*}C(−1,4) with \begin{align*}k=\frac{3}{2}\end{align*}k=32 .
Algebra Connection Find the value of the missing variable(s).
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9692.