# Ch 9: Geometry Basics for Precalculus

### About This Chapter

## Geometry Basics for Precalculus - Chapter Summary and Learning Objectives

Watch the videos included in this chapter to learn how the geometric theorems and formulas used to find measurements for basic shapes, like circles and triangles, can also be used to calculate the volume of cylinders and spheres. Instructors show you how some of these geometry basics apply to trigonometry as well. Lessons are designed to teach you how to:

- Graph circles and determine their area and circumference
- Calculate the distance and midpoint between two line segments
- Determine the area and perimeter of two-dimensional shapes
- Find the volume of basic three-dimensional shapes
- Solve for unknown sides of right and non-right triangles

Video | Objectives |
---|---|

Circles: Area and Circumference | Learn formulas for calculating the area and circumference of a circle. Determine the surface area and volume of a cylinder. |

Graphing Circles: Identifying the Formula, Center and Radius | Get tips for graphing and writing the formula for a circle. |

Write the Standard Form of an Equation by Completing the Square | Practice completing the square and converting a quadratic equation into standard form. |

How to Use the Distance Formula | Use this formula to calculate the distance between two points on a graph. |

How to Use the Midpoint Formula | Find out how to determine the midpoint of a line segment. |

How to Solve Visualizing Geometry Problems | Visualize geometry problems using hands-on and graphical approaches. |

How to Calculate the Volumes of Basic Shapes | Learn how to calculate the area and perimeter of two-dimensional shapes. Calculate the volume of three-dimensional shapes. |

Finding Distance with the Pythagorean Theorem | Use the Pythagorean theorem to solve non-right triangles. |

Trigonometry and the Pythagorean Theorem | Understand how trigonometric functions and the Pythagorean theorem can be used to solve right triangles. |

### 1. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

### 2. Graphing Circles: Identifying the Formula, Center and Radius

Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.

### 3. Write the Standard Form of an Equation by Completing the Square

In math, we have a process called completing the square where you take your quadratic equation and rewrite it to make it easier to solve. Watch this video lesson to learn how you can do this process easily yourself.

### 4. How to Use The Distance Formula

You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!

### 5. How to Use The Midpoint Formula

The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.

### 6. How to Solve Visualizing Geometry Problems

A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.

### 7. How to Calculate the Volumes of Basic Shapes

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

### 8. Finding Distance with the Pythagorean Theorem

How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.

### 9. Trigonometry and the Pythagorean Theorem

Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.

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### Other Chapters

Other chapters within the Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Continuity
- Limits in Precalculus