About This Chapter
Honors Geometry: Properties of Polygons & Circles - Chapter Summary and Learning Objectives
Use the lessons in this chapter to learn about the properties and measurements of circles and various polygons. We strive to keep the learning experience enjoyable, so you'll find engaging videos included with each lesson. Use the videos' transcripts as a resource for taking notes. As you complete the lessons, take self-assessment quizzes to see how well you've retained the information. Take a cumulative chapter exam at the end to test your knowledge of the topics. If you need additional help, reach out to the instructor. In this chapter, you'll explore:
- Properties of polygons including rectangles, squares, trapezoids, and more
- Proof theorems for parallelograms
- Measurements of angles and lengths involving tangents, chords and secants
- The tangent of a circle
|Geometric Proofs for Polygons||Learn about proofs used in geometry.|
|Properties of Shapes: Rectangles, Squares and Rhombuses||Discover properties of rectangles, squares and rhombuses|
|Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons||Compare quadrilaterals, parallelograms, trapezoids and polygons.|
|Parallelograms: Definition, Properties, and Proof Theorems||Figure out how to identify parallelograms.|
|Properties of Congruent and Similar Shapes||Explore components of similar and congruent shapes.|
|Inscribed and Circumscribed Figures: Definition & Construction||Examine inscribed and circumscribed figures.|
|Central and Inscribed Angles: Definitions and Examples||Consider theorems for central and inscribed angles.|
|Measurements of Angles Involving Tangents, Chords & Secants||Uncover ways to measure angles involving tangents, chords and secants.|
|Measurements of Lengths Involving Tangents, Chords and Secants||Learn to measure lengths involving tangents, chords and secants.|
|Tangent of a Circle: Definition & Theorems||Develop an understanding of the tangent of a circle.|
1. Geometric Proofs for Polygons
Watch this video lesson to learn why it is important for you to learn how to do formal proofs in geometry. Also learn how to set up a proof and how to successfully execute one.
2. Properties of Shapes: Rectangles, Squares and Rhombuses
What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.
3. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons
Four-sided objects are more than just squares and rectangles. In this lesson, we'll discuss quadrilaterals, parallelograms and trapezoids. We'll also discuss polygons, objects that can have more sides than you can count.
4. Parallelograms: Definition, Properties, and Proof Theorems
Watch this video lesson to learn how you can identify parallelograms. You will see the unique properties that belong to the parallelogram. You will see the special side and angle characteristics needed to prove a certain shape is a parallelogram.
5. Properties of Congruent and Similar Shapes
In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.
6. 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.
7. Central and Inscribed Angles: Definitions and Examples
When we're working with circles, there are two key angles to know: central angles and inscribed angles. These angles have a few special theorems, which we'll discuss and practice using in this lesson.
8. 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.
9. 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.
10. 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.
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 within the Honors Geometry Textbook course
- Honors Geometry: Foundations of Geometry
- Honors Geometry: Fundamentals of Geometry Proofs
- Honors Geometry: Logic in Mathematics
- Honors Geometry: Introduction to Geometric Figures
- Honors Geometry: Properties of Triangles
- Honors Geometry: Similar & Congruent Triangle Proofs
- Honors Geometry: Right Triangle Proofs
- Honors Geometry: Relationships Within Triangles
- Honors Geometry: Parallel Lines & Polygons
- Honors Geometry: Parallel Line Proofs
- Honors Geometry: Coordinate Geometry
- Honors Geometry: Analytical Geometry
- Honors Geometry: Similar Polygons
- Honors Geometry: Polygons & Quadrilaterals
- Honors Geometry: Circular Arcs & Circles
- Honors Geometry: Conic Sections
- High School Geometry: Geometric Solids
- Honors Geometry: Introduction to Trigonometry
- Honors Geometry: Right Triangles & Trigonometry
- Honors Geometry: Area, Surface Area & Volume
- Honors Geometry: Perimeter & Circumference
- Honors Geometry: Transformations
- Honors Geometry: Matrices