# Chapter 6: Geometry and Transformations

**Basic**Created by: CK-12

## Introduction

Here you will learn some basic topics of geometry. First you will learn all about angles, including identifying types of angles and measuring angles. Then you will learn how to classify polygons. Next you will learn the concepts of congruence and similarity as they relate to geometry. Finally, you will learn about the geometric transformations of reflection, translation, rotation, and dilation, and you will see how these transformations relate to congruence and similarity.

## Chapter Outline

- 6.1. Identify Angle Pairs
- 6.2. Identify Adjacent and Vertical Angles
- 6.3. Identify Types of Lines
- 6.4. Measures of Angle Pairs
- 6.5. Classifying Triangles
- 6.6. Understanding the Angle Measures of Triangles
- 6.7. Classifying Quadrilaterals
- 6.8. Understanding the Angle Measures of Quadrilaterals
- 6.9. Identifying Polygons
- 6.10. Recognizing and Understanding Congruent Polygons
- 6.11. Identify and Apply Theorems to Triangle Congruence
- 6.12. Recognizing Reflections
- 6.13. Identify Lines of Symmetry
- 6.14. Recognizing Translation Transformations
- 6.15. Recognizing Rotation Transformations
- 6.16. Identifying Tessellations
- 6.17. Recognizing Similarity
- 6.18. Recognizing Dilations

### Chapter Summary

## Summary

You learned that two angles are complementary if the sum of their measures is \begin{align*}90^\circ\end{align*} and two angles are supplementary if the sum of their measures is \begin{align*}180^\circ\end{align*}. You also learned to identify vertical angles and that vertical angles are always congruent. You then learned about lines and how lines can be parallel, perpendicular, or neither.

Next you focused on polygons, and learned how to accurately classify triangles, quadrilaterals, and other polygons. You learned that two shapes are congruent if they are exactly the same shape and the same size. Two shapes are similar if they are exactly the same shape but not necessarily the same size.

Finally, you learned about the geometric transformations of reflection, rotation, translation, and dilation. You learned that reflections, rotations, and translations all produce congruent shapes, while dilations produce similar shapes. You also learned about tessellations, and how to determine whether or not a regular polygon will tessellate.