Ch 26: Introduction to Proofs and Constructions

About This Chapter

Use our video lessons and quizzes to help you understand geometric postulates. Learn to prove theorems for parallelograms, triangles, lines and angles.

Introduction to Proofs and Constructions - Chapter Summary

If you're looking to get a better idea of the differences between proofs, theorems and postulates, this chapter is for you. Introductory lessons explain what theorems are used for and introduce you to the axiomatic systems and postulates used to derive them.

You can build on this knowledge to explore theorems relating to corresponding pairs of angles and sides as well as parallel or perpendicular lines. Instructors also walk you through the various postulates used to demonstrate the congruence of triangles or establish the relationships between triangle medians, midsegments and centroids.

You can also take a look at parallelogram theorems used to prove the congruence of opposite sides and angles, the supplementary nature of consecutive angles and the shapes formed by their diagonals. This chapter concludes with lessons that show you how to apply this knowledge by using compasses and rulers to create geometric shapes, such as equilateral triangles, squares, triangles and inscribed hexagons. Topics of instruction include:

  • Axiomatic systems
  • Triangle congruence postulates
  • Postulates for lines and angles
  • Triangle theorems
  • Parallelogram theorems

Whether you choose to access lesson content in the form of short videos or corresponding transcripts, you'll get the benefit of our instructors' expertise. This chapter also includes self-checking, multiple-choice quizzes you can take as many times as you need.

9 Lessons in Chapter 26: Introduction to Proofs and Constructions
Test your knowledge with a 30-question chapter practice test
The Axiomatic System: Definition & Properties

1. The Axiomatic System: Definition & Properties

Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.

Postulates & Theorems in Math: Definition & Applications

2. Postulates & Theorems in Math: Definition & Applications

In this lesson, we will define postulates and theorems in mathematics. We will look at examples of postulates and theorems and how to use them in mathematics and in real-world applications.

Interior Angle Theorem: Definition & Formula

3. Interior Angle Theorem: Definition & Formula

This lesson will define what an interior angle is, and it will provide and explain how to use the formula for finding the sum of the interior angles of a polygon. Examples will be provided detailing four of the ways it can be used.

Alternate Interior Angles: Definition, Theorem & Examples

4. Alternate Interior Angles: Definition, Theorem & Examples

In this lesson, you will learn how to identify alternate interior angles and how to use the theorem to find missing angles and to solve everyday geometry problems.

Supplementary Angle: Definition & Theorem

5. Supplementary Angle: Definition & Theorem

There are many important angle pairs in geometry. In this lesson, we'll learn about supplementary angles, including what they are, where they are used, and why you need to know about them.

Corresponding Angles: Definition, Theorem & Examples

6. Corresponding Angles: Definition, Theorem & Examples

In this lesson, you will learn how to identify corresponding angles. You will also learn how to use a theorem to find missing angles and solve everyday geometry problems.

Geometric Proofs: Definition and Format

7. 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

8. 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.

Practice Making Geometric Constructions with Tools

9. Practice Making Geometric Constructions with Tools

There are a number of tools available to geometry students to help make their work a bit easier. In this lesson, we will review how to use many of them in order for you to get the most out of every geometry class.

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