### Unit 1: The Basics of Geometry

From a young age, we learn basic vocabulary and basic concepts that lead us to understand greater concepts. In this unit, you will learn about the basic building blocks of Geometry.

Everything has a proper name. We often seem to use nicknames: "fridge" instead of "refrigerator," "phone" instead of "telephone," and so on. Still, we know what the proper terminology is, even if we do not use it as often as we probably should. Knowing the meanings of several basic terms in Geometry is important, because these terms are going to keep popping up over and over again. Whether it is knowing a simple definition, or understanding the relationships between angles, these basic items are a "must know" in Geometry.

In life, we also classify things. We tend to classify by height, age, weight, food preference, nationality, etc. We will use pretty much anything we can think of for classification purposes. While some classifications might seem unnecessary to us, others seem quite important. Classifying berries, for example, can help you to keep from eating a poisonous one that would make you sick. Without classification, we would not have a way to keep the good ones separate from the bad ones. The same holds true in Geometry. Classifying shapes like triangles can help us recognize these shapes faster and eventually recognize the rules and relationships pertaining to their classification.

**Completing this unit should take you approximately 15 hours.**

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

- define and identify angles, rays, line segments, and points, based on the undefined notions of point, line, distance along a line, and distance around a circular arc;
- determine the distance between two points;
- determine the lengths of a line segment's sections;
- measure and classify angles;
- determine the measurement of unknown angles; and
- classify polygons by sides.

### 1.1: Language and Notation of Basic Geometry

Take notes as you watch this video to learn about the language and notation of basic geometry including line, line segment, ray, midpoint, collinear, and planar. Watch the presentation carefully two or three times until you are able to explain how to understand the terminology and notation associated with these terms.

Take notes as you watch this video to learn about how to identify the differences between a line, line segment, and a ray. Watch the presentation carefully two or three times until you are able to explain how to understand the differences with these terms.

Study the "Points, Lines, and Planes" section. This section provides examples and definitions of point, line, plane, space, segment rays, postulates, and draw diagrams. Then, complete questions 1-10. These questions will provide you with the opportunity to identify general geometry terms and draw diagrams. The solutions to these problems are located in the "Answers" section.

Complete this assessment, which tests your knowledge on basic geometry terminology. You can review the concepts associated with these questions with the Khan videos in subunit 1.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete this assessment, which tests your knowledge on basic geometry terminology. You can review the concepts associated with these questions with the Khan videos in subunit 1.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 1.2: Distance between Two Points

Take notes as you read this section and watch the embedded videos to learn about the distance between two points and the segment addition postulate. Watch the presentations carefully two or three times until you are able to explain how apply finding the distance between two points and the segment addition postulate. This section provides examples of measuring on a ruler and finding the distance between points.

Select the "Practice" tab, and complete the activity on the distance between two points and the angle addition postulate. Compute the answer to the given problem, and select your response. Click on "Submit Answer" to see if you choose the correct or an incorrect answer. Then, click on "Next" to move on to another question. You have completed the activity when you see "You have reached the maximum practice questions." (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.)

### 1.3: Midpoints and Segment Bisectors

Take notes as you read this section and watch the video to learn about midpoints and segment bisectors. This section provides examples of measuring on a ruler and finding the distance between points.

Select the "Practice" tab, and complete the activity on the midpoints and segment bisectors. Compute the answer to the given problem, and select your response. Click on "Submit Answer" to see if you choose the correct or an incorrect answer. Then, click on "Next" to move on to another question. You have completed the activity when you see "You have reached the maximum practice questions." (Note: You can refresh the page if you would like additional practice problems and the questions will be different than the first set.)

### 1.4: Angles

### 1.4.1: Angle Basics

Take notes as you watch this video to learn about the language and notation of angles. Watch the presentation carefully two or three times until you are able to explain how to understand the terminology and notation associated with these terms.

### 1.4.2: Measuring Angles

Take notes as you watch these videos to learn about how to use a protractor and to measure angles in degrees. Watch the presentations carefully two or three times until you are able to measure an angle with a protractor and measuring angles in degrees.

Read this section, which provides examples of measuring with a protractor and understanding the angle addition postulate.

Scroll down to the "Review" section, and complete exercises 1-17. These exercises will provide you with the opportunity to use the angle addition postulate, properties of angles, and draw and measure .

### 1.4.3: Congruent Angles and Angle Bisectors

Take notes as you read this section and watch the videos to learn about angle bisectors. This section provides examples identifying congruent angles and applying properties of an angle bisector.

These exercises will provide you with the opportunity to use properties of congruent angles and angle bisectors.

### 1.4.4: Acute, Obtuse, and Right Angles

Take notes as you watch these videos to learn how to identify acute, right, and obtuse angles. Watch the presentations carefully two or three times until you are able to identify types of angles.

Complete this assessment, which tests your knowledge on types of angles. You can review the concepts associated with these questions with the Khan videos in subunit 1.4.4.

### 1.4.5: Complementary and Supplementary Angles

Take notes as you watch these videos to learn how to identify supplementary and complementary angles. Watch the first presentation carefully to understand the basics of complementary, supplementary, adjacent, and straight angles. Watch the second presentations carefully two or three times until you are able to identify types of angles.

- Complete the problems on complementary angles. You can refresh the page if you would like additional practice problems, and the questions will be different than the first set.
- Complete the problems on supplementary angles. You can refresh the page if you would like additional practice problems, and the questions will be different than the first set.
Complete this assessment, which tests your knowledge on complementary and supplementary angles. You can review the concepts associated with these questions with the Khan videos in subunit 1.4.5.

### 1.4.6: Linear Pairs

Take notes as you read this section and watch the videos to learn about linear pairs. This section provides examples of adjacent angles and angles that form a linear pair. Then, complete exercises 1-16 under "Explore more". These exercises will provide you with the opportunity to determine angles using linear pairs. Once you have completed the exercises, check your answers against the linked answer key.

### 1.4.7: Vertical Angles

Take notes as you watch this video to learn how vertical angles are equal to each other. Watch the presentation carefully two or three times to understand how vertical angles are equal.

Take notes as you read this section and watch videos to learn about linear pairs. This section provides examples of vertical angles and the vertical angles theorem. Then, complete exercises 1-14 under "Explore More". These exercises will provide you with the opportunity to determine angles using vertical angles. Once you have completed the exercises, check your answers against the linked answer key.

Complete this assessment, which tests your knowledge on vertical angles. You can review the concepts associated with these questions with the Khan videos in subunit 1.4.7.

### 1.5: Polygon Classification

Study the "Points, Lines, and Planes" section. This section provides examples of various polygons and concave and convex polygons. Then, complete questions 1-14. These questions will provide you with the opportunity to identify polygons and apply polygon properties.