About This Chapter
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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