# Chapter 1: Basics of Geometry

**At Grade**Created by: CK-12

## Introduction

In this chapter, students will learn about the building blocks of geometry. We will start with the basics: point, line and plane and build upon those terms. From here, students will learn about segments, midpoints, angles, bisectors, angle relationships, and how to classify polygons.

- 1.1.
## Basic Geometric Definitions

- 1.2.
## Distance Between Two Points

- 1.3.
## Congruent Angles and Angle Bisectors

- 1.4.
## Midpoints and Segment Bisectors

- 1.5.
## Angle Measurement

- 1.6.
## Angle Classification

- 1.7.
## Complementary Angles

- 1.8.
## Supplementary Angles

- 1.9.
## Linear Pairs

- 1.10.
## Vertical Angles

- 1.11.
## Triangle Classification

- 1.12.
## Polygon Classification

### Chapter Summary

## Summary

This chapter begins with the basic components of Euclidean Geometry. From the introductory definition of points, lines, and planes it builds to a discussion of classifying figures such as angles, triangles, and polygons. Measurement of distances and angles are also covered. Different types of angle relationships are compared and explored, such as complementary angles, supplementary angles and linear pairs.

### Symbol Toolbox for Chapter

\begin{align*}\overleftrightarrow{AB}, \ \overrightarrow{AB}, \ \overline{AB}\end{align*} Line, ray, line segment

\begin{align*}\angle ABC\end{align*} Angle with vertex \begin{align*}B\end{align*}

\begin{align*}m \overline{AB} \ \text{or} \ AB\end{align*} Distance between \begin{align*}A\end{align*} and \begin{align*}B\end{align*}

\begin{align*}m \angle ABC\end{align*} Measure of \begin{align*}\angle ABC\end{align*}

\begin{align*}\bot\end{align*} Perpendicular

\begin{align*}=\end{align*} Equal

\begin{align*}\cong\end{align*} Congruent

### Chapter Keywords

- Geometry
- Point
- Line
- Plane
- Space
- Collinear
- Coplanar
- Endpoint:
- Line Segment
- Ray
- Intersection
- Postulates
- Theorem
- Distance
- Measure
- Ruler Postulate
- Segment Addition Postulate
- Angle
- Vertex
- Sides
- Protractor Postulate
- Straight Angle
- Right Angle
- Acute Angles
- Obtuse Angles
- Perpendicular
- Construction
- Compass
- Angle Addition Postulate
- Congruent
- Midpoint
- Midpoint Postulate
- Segment Bisector
- Perpendicular Bisector
- Perpendicular Bisector Postulate
- Angle Bisector
- Angle Bisector Postulate
- Complementary
- Supplementary
- Adjacent Angles
- Linear Pair
- Linear Pair Postulate
- Vertical Angles
- Vertical Angles Theorem
- Triangle
- Right Triangle
- Obtuse Triangle
- Acute Triangle
- Equiangular Triangle
- Scalene Triangle
- Isosceles Triangle
- Equilateral Triangle
- Polygon
- Diagonals

### Chapter Review

Match the definition or description with the correct word.

Definition/Description | Answer |
---|---|

1. When three points lie on the same line. | A. Measure |

2. All vertical angles are ________. | B. Congruent |

3. Linear pairs add up to _______. | C. Angle Bisectors |

4. The \begin{align*}m\end{align*} in from of \begin{align*}m \angle ABC\end{align*}. | D. Ray |

5. What you use to measure an angle. | E. Collinear |

6. When two sides of a triangle are congruent. | F. Perpendicular. |

7. \begin{align*}\bot\end{align*} | G. Line |

8. A line that passes through the midpoint of another line. | H. Protractor |

9. An angle that is greater than \begin{align*}90^\circ\end{align*}. | I. Segment Addition Postulate. |

10. The intersection of two planes is a ___________. | J. Obtuse |

11. \begin{align*}AB + BC = AC\end{align*} | K. Point |

12. An exact location in space. | L. \begin{align*}180^\circ\end{align*} |

13. A sunbeam, for example | M. Isosceles |

14. Every angle has exactly one. | N. Pentagon |

15. A closed figure with 5 sides. | O. Hexagon |

P. Bisector |

### Texas Instruments Resources

*In the CK-12 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/9686.*