# Ch 1: Introduction to Basic Geometry

### About This Chapter

## Who's It For?

Anyone who needs help learning or mastering basic geometry material will benefit from the lessons in this chapter. There is no faster or easier way to learn basic geometry. Among those who would benefit are:

- Students who have fallen behind in understanding basic geometry
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about basic geometry
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How It Works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Introduction to Basic Geometry chapter exam.

## Why It Works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the Introduction to Basic Geometry chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any basic geometry question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

## Students Will Review:

This chapter helps students review the concepts in a basic geometry unit of a standard geometry course. Topics covered include:

- Overview of the origins of geometry and how it has changed over time
- Inductive and deductive reasoning
- Postulates and algebraic laws that form the basis for geometry
- Applying direct and geometric proofs

### 1. What is Geometry?

Geometry can be traced all the way back to 2000 BC. Watch this video lesson and learn how much geometry has grown over time, and how people from Egypt, Greece, and France have contributed to the geometry we now use today.

### 2. Inductive & Deductive Reasoning in Geometry: Definition & Uses

Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.

### 3. Properties and Postulates of Geometric Figures

In geometry, there are some basic postulates that are relied upon as the basis for other theorems. Watch this video to learn about the postulates that deal with points, lines, and planes.

### 4. Algebraic Laws and Geometric Postulates

Watch this video to learn about the basic algebraic laws that are also part of the basic geometric postulates that form the basis for the geometry that we know and study today.

### 5. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

### 6. Geometric Proofs: Definition and Format

Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.

### 7. How to Create a Coordinate Plane

In this lesson, we'll first learn the various elements of a coordinate plane, after which we'll learn how to create a coordinate plane. We will also look at how to locate points on the coordinate plane and where the coordinate plane came from.

### 8. How to Find Area from Diameter

In this lesson, we will review what the diameter and the radius of a circle are and then look at how these two characteristics are related to one another. We will use this information to find a formula that enables us to find the area of a circle given its diameter.

### 9. How to Find the Distance between Two Planes

In this lesson we show how to find the distance between two planes. You will see how to determine the parameters for substituting into the distance formula.

### 10. Brahmagupta's Formula: Proof & Examples

In this lesson, we'll explore a derivation of a simple but powerful formula for finding the area of some special quadrilaterals. Examples will be provided to show how this formula is used.

### 11. Brocard Diameter: Definition & Formula

Brocard diameters are a really neat characteristic that triangles possess. This lesson will define the Brocard diameter of a triangle. We will also look at how to find its length, and do so in a real world application.

### 12. Butterfly Theorem: History & Applications

The butterfly theorem and its applications have kept mathematicians fascinated for many years. We will take a look at this theorem, explore its history a bit, and discuss its application in various areas.

### 13. Cardioid in Math: Definition, Equation & Examples

This lesson will cover a neat shape studied in upper-level mathematics called a cardioid. We will look at the basic shape, how it is constructed, its equation in polar form, and various examples of these equations and corresponding cardioids.

### 14. How to Plot Cassini Ovals

The process of plotting Cassini ovals is the same as any other mathematical curve. This lesson will explain the process of plotting Cassini ovals using equations and specific values within the equation. We will also use an example to practice.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Basic Geometry: Help & Review course

- Geometry Topics
- Basic Geometry: Lines & Angles
- Basic Geometry: Polygons
- Basic Geometry: Triangles
- Basic Geometry: Quadrilaterals
- Basic Geometry: Circles
- Basic Geometric Constructions
- Basic Geometry: Similar Figures
- Basic Geometry: Perimeter, Circumference & Area
- Basic Geometry: 3-Dimensional Figures
- Lines and Angles in Geometry
- Perimeter, Area & Volume
- Geometric Properties of Objects
- Geometric Graphing Basics
- Geometric Graphing Functions