About This Chapter
Circles, Angles and Circular Arcs - Chapter Summary and Learning Objectives
Circles are so plentiful around us that we often don't give them another thought. In this chapter, you can review measurement calculations for circles, learn the difference between major and minor arcs and find out how to construct figures inside and outside of other figures. You can also find out more about measuring angles involving secants, tangents and chords. In these lessons, you'll learn things like:
- What's the difference between circumference and area of circles?
- Where are inscribed and circumscribed figures located?
- How can I measure inscribed angles?
- When is a polygon 'regular'?
- How do I measure angles and lengths involving chords, tangents and secants?
|Circles: Area and Circumference||Calculate the circumference and area of circles.|
|Inscribed and Circumscribed Figures: Definition & Construction||Construct circumscribed and inscribed figures.|
|How to Find the Measure of an Inscribed Angle||Measure inscribed angles.|
|Tangent of a Circle: Definition & Theorems||Understand the theorems for tangents of circles.|
|Arc Length of a Sector: Definition and Area||Measure the arc length of sectors.|
|Measurements of Angles Involving Tangents, Chords & Secants||Measure angles having tangents, secants and chords.|
|Measurements of Lengths Involving Tangents, Chords and Secants||Discover the lengths when chords, tangents and secants are involved.|
|Regular Polygons: Definition & Parts||Find out what makes a polygon regular and learn about the parts of polygons.|
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. 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 Algebra 2 and Trig Textbook course
- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities