Copyright

Ch 13: Principles of Euclidean Geometry

About This Chapter

Check out the video lessons included in this engaging chapter on the principles of Euclidean geometry to help you finish your homework or study for a test. These videos are easy to navigate, coupled with short quizzes and accessible to you 24 hours a day.

Principles of Euclidean Geometry - Chapter Summary

The principles of Euclidean geometry are laid out clearly for your review in this informative chapter. You'll study the rules and formulas of basic geometry, as well as how to solve problems with measurement. After completing this chapter, you should be ready to:

  • Define indirect measurement with examples
  • Differentiate between Euclidean and non-Euclidean geometry
  • Explain the developments and postulates of Euclid's axiomatic geometry
  • Outline the properties of different shapes
  • Identify triangle congruence postulates
  • Provide the definition and format for geometric proofs
  • Explain tools and methods for making geometric constructions

Even if you've struggled with these topics before, our chapter makes it easy to understand these subjects as you study on any tablet, mobile phone or computer. Along the way, feel free to reach out to one of our instructors for assistance if you have any questions, and take the quizzes provided with each lessons to clarify these topics and see if you're ready to move on.

9 Lessons in Chapter 13: Principles of Euclidean Geometry
Test your knowledge with a 30-question chapter practice test
Basic Geometry: Rules & Formulas

1. Basic Geometry: Rules & Formulas

In this lesson, we'll go over some of the basic formulas and rules in geometry, the study of shapes and space. You'll learn formulas to find the perimeter, area, volume, and surface area of two-dimensional and three-dimensional shapes.

How to Solve Problems with Measurement

2. How to Solve Problems with Measurement

In this lesson, we will use basic mathematical operations to solve problems involving perimeter, area, and volume. You will also learn a method for scaling to compare models to real structures or objects.

Indirect Measurement: Definition & Examples

3. Indirect Measurement: Definition & Examples

Learn what indirect measurement is and see what is involved when we use this measuring tool. Become comfortable applying indirect measurement through explanation and examples.

Differences Between Euclidean & Non-Euclidean Geometry

4. Differences Between Euclidean & Non-Euclidean Geometry

Euclidean geometry is the study of the geometry of flat surfaces, while non-Euclidean geometries deal with curved surfaces. Here, we'll learn about the differences between these mathematical systems and the different types of non-Euclidean geometry.

Euclid's Axiomatic Geometry: Developments & Postulates

5. Euclid's Axiomatic Geometry: Developments & Postulates

Learn how the way we do proofs in geometry had its start with Euclid in this video lesson. Learn about his contributions to the geometry we know today. Also learn about the five basic truths that he used as a basis for all other teachings.

Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons

6. 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.

Triangle Congruence Postulates: SAS, ASA & SSS

7. Triangle Congruence Postulates: SAS, ASA & SSS

When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.

Geometric Proofs: Definition and Format

8. 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.

Methods & Tools for Making Geometric Constructions

9. Methods & Tools for Making Geometric Constructions

Did you know that it's possible to do math without using numbers? This is exactly what Euclid did when he showed how to solve mathematical problems by drawing them out instead of with numbers.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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.

Support