About This Chapter
Circular Arcs, Circles and Angles - Chapter Summary and Learning Objectives
The lessons in this chapter explore the similarities and differences among circles, circular arcs and angles. We'll learn about formulas that help us measure these structures and look at methods of deriving equations that show various properties. Also included are practice lessons that give you experience working with some of these figures. When you've viewed all these lessons, you should be able to:
- Use the Pythagorean theorem
- Determine the measure of angles formed by tangents
- Use formulas to measure a circle's area and circumference
- Determine measurements that involve secants, tangents and chords
- Identify a polygon
|Similarity of Circles||We'll examine the like properties of all circles.|
|Circles: Area and Circumference||This lesson explores the formulas that show the area and circumference of circles.|
|Circles: Inscribed Angles, Radii, Chords||Here, we'll define and examine inscribed angles, chords and radii.|
|Practice with Inscribed Angles, Radii, Chords||You'll gain experience through exercises that show the relationships between inscribed angles, radii and chords.|
|Inscribed and Circumscribed Figures||We'll see what these figures are and look at their relationship.|
|Measure of an Inscribed Angle||This lesson examines how to calculate the measure of an inscribed angle.|
|Constructing Inscribed and Circumscribed Triangles and Quadrilaterals||Here, we'll see what forms an inscribed and circumscribed triangle and quadrilateral.|
|Proofs for Inscribed and Circumscribed Triangles and Quadrilaterals||In this lesson, we'll develop proofs to show the properties of angles inscribed in a circle.|
|Tangent of a Circle||We'll learn about forming a tangent line to a circle.|
|Arc Length of a Sector: Definition and Area||This lesson shows what a sector is and how to find its area. You'll also learn the definition of arc length.|
|Arc Length and Radians||We'll learn to measure arc length using radians in this lesson.|
|Deriving the Equation of a Circle||This lesson shows us how to use the Pythagorean theorem to derive the equation of a circle.|
|Find the Center and Radius of a Circle by Completing the Square||This video lesson explains how to derive an equation using the Pythagorean theorem as well as how to complete the square to find the circle's center and radius.|
|Measurements of Angles Involving Tangents, Chords and Secants||We'll learn to determine the angles formed by tangents and determine the lengths of segments involved by tangents.|
|Measurements of Lengths Involving Tangents, Chords and Secants||We'll learn to find lengths involving tangents, chords and secants.|
|Regular Polygons||Here, we'll find out how to identify a polygon and its components.|
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. In this lesson, learn how to find the area and circumference of circles by working through several examples.
2. Inscribed and Circumscribed Figures: Definition & Construction
A square and a circle may be different shapes, but they still can have a unique relationship. In this lesson, we'll learn about inscribed and circumscribed figures.
3. How to Find the Measure of an Inscribed Angle
Finding the measure of an inscribed angle requires knowing a little information. In this lesson, we'll find the measure of an inscribed angle when we know the measure of the central angle or one or more of the arcs formed by the angle.
4. Tangent of a Circle: Definition & Theorems
What happens when a line just barely touches a circle? It's a tangent! In this lesson, we'll learn all about tangents to circles, including a few key theorems. We'll also look at tangent circles.
5. Arc Length of a Sector: Definition and Area
In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths.
6. Measurements of Angles Involving Tangents, Chords & Secants
When lines and circles meet, angles are formed. Fortunately, we can determine the measure of these angles, whether they're formed by tangents, secants or chords, just by knowing the measure of the created arcs.
7. Measurements of Lengths Involving Tangents, Chords and Secants
The lengths of chords, tangents and secants take on unique relationships when they're drawn on circles. In this lesson, we'll define those relationships and see them in action.
8. Regular Polygons: Definition & Parts
What makes a polygon a polygon? And what shapes are considered polygons? In this lesson, find out the answers to these questions and more as we learn all about polygons and their parts.
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Other chapters within the Trigonometry: High School course
- Real Numbers: Types and Properties
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Coordinate Geometry Review
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Functions for Trigonometry
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions Review
- Polynomial Functions Basics
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Triangle Trigonometry
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations
- Teaching Resources for High School Trigonometry