### Unit 6: Similarity

In this unit, you will review ratios and proportions, and you will learn how they connect to similarity. In the real world, you may see an item and think that it is similar to something else, whether it is because of the design, the size, or some other factors. In Geometry, however, similarity has very strict rules attached to it. You will learn to apply these rules to determine if two shapes, especially triangles, are similar.

**Completing this unit should take you approximately 14 hours.**

Upon successful completion of this unit, you will be able to:

- determine whether two triangles are similar;
- write and identify accurate similarity statements; and
- use proportions to solve problems.

### 6.1: Similar Polygons

Take notes as you watch this video to understand properties of similar triangles. Watch this presentation carefully two or three times to understand what the relationship is between sides and angles of similar figures.

Take notes as you watch the videos and read this section to learn about similar polygons and scale factor. This section provides examples of applying these properties to similar figures. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the properties of similar figures.

Complete this assessment, which tests your knowledge of similar triangles and their properties. You can review the concepts associated with these questions with the content from subunit 6.1.

Complete this assessment, which tests your knowledge of similar triangles and their properties. You can review the concepts associated with these questions with the content from subunit 6.1.

### 6.2: Similarity Postulates

Take notes as you watch this video to understand postulates of similar triangles. Watch this presentation carefully two or three times to understand how to determine similarity postulates of similar triangles.

### 6.2.1: Angle-Angle (AA) Similarity and Indirect Measurement

Take notes as you watch this video to understand sample problems of similar triangles. Watch this presentation carefully two or three times to understand how to find missing sides and angles of similar triangles.

Read this section, which provides examples of how to prove triangles are similar by AA and how to indirectly measure items. Then, complete the practice problems. These exercises will provide you with the opportunity to apply AA similarity and indirect measurement.

### 6.2.2: Side-Side-Side (SSS) Similarity and Side-Angle-Side (SAS) Similarity

Read this section, which provides examples of how to prove triangles are similar by SSS and how to find missing parts of similar triangles. Then, complete the practice problems. These questions will provide you with the opportunity to apply SSS similarity.

Read this section, which provides examples of how to prove triangles are similar by SAS and how to find missing parts of similar triangles. Then, complete the practice problems. These questions will provide you with the opportunity to apply SAS similarity.

### 6.3: Triangle Proportionality and Parallel Lines and Transversals

Take notes as you watch this video to understand sample problems of similar triangles. Watch this presentation carefully two or three times to understand how to find missing sides and angles of similar triangles.

Read this section, which provides examples of how to find missing parts of similar triangles in other forms. Then, complete the practice problems. These questions will provide you with the opportunity to apply proportionality relationships.

Complete this assessment, which tests your knowledge on finding missing sides and angles of similar triangles. You can review the concepts associated with these questions with the content from subunits 6.2 and 6.3.

Complete this assessment, which tests your knowledge on finding missing sides and angles of similar triangles. You can review the concepts associated with these questions with the content from subunits 6.2 and 6.3.

### 6.4: Proportions with Angle Bisectors

Take notes as you watch the videos and read this section to learn about proportions with angle bisectors in triangles. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the properties of the triangle angle bisectors theorem.