Copyright

Ch 39: MTEL Mathematics (Elementary): Proof of Theorems

About This Chapter

Refresh your knowledge of key geometry theorems as you study for the MTEL Elementary Mathematics exam. In this chapter, you'll find a number of helpful video lessons that will quickly get you up to speed on a number of theorems.

MTEL Elementary Mathematics: Proof of Theorems - Chapter Summary

Proof of theorems is introduced in this chapter of the study guide. These lessons provide an introduction to the subject, including applications of similar triangles, triangle congruence postulates, and congruence proofs. The converse of a statement, and congruency are also covered by the lessons in this Proof of Theorems chapter. Other topics in this chapter include:

  • Midpoint theorem
  • Proof by contradiction
  • Properties of right triangles
  • Special right triangles
  • The Pythagorean theorem
  • The hypotenuse angle, hypotenuse leg, and angle-angle-side theorems

Knowledgeable instructors walk you through each subject using short, engaging video lessons, and are available to answer any questions you may have. Videos are accompanied by transcripts with important terms bolded, to help you study. The jump feature under the Timeline tab allows you to skip directly to main subjects within the videos, so you can review the subjects you need the most help with.

15 Lessons in Chapter 39: MTEL Mathematics (Elementary): Proof of Theorems
Test your knowledge with a 30-question chapter practice test
Applications of Similar Triangles

1. Applications of Similar Triangles

Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.

Triangle Congruence Postulates: SAS, ASA & SSS

2. 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.

Congruence Proofs: Corresponding Parts of Congruent Triangles

3. Congruence Proofs: Corresponding Parts of Congruent Triangles

Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.

Converse of a Statement: Explanation and Example

4. Converse of a Statement: Explanation and Example

Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.

The AAS (Angle-Angle-Side) Theorem: Proof and Examples

5. The AAS (Angle-Angle-Side) Theorem: Proof and Examples

When trying to find out if triangles are congruent, it's helpful to have as many tools as possible. In this lesson, we'll add to our congruence toolbox by learning about the AAS theorem, or angle-angle-side.

The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

6. The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

In this lesson, we'll learn about the hypotenuse angle theorem. With this theorem, we can prove two right triangles are congruent with just congruent hypotenuses and acute angles.

The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

7. The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

In this lesson, we'll learn about the hypotenuse leg theorem. This theorem enables us to prove two right triangles are congruent based on just two sides.

Congruency of Right Triangles: Definition of LA and LL Theorems

8. Congruency of Right Triangles: Definition of LA and LL Theorems

In this lesson, we'll learn two theorems that help us prove when two right triangles are congruent to one another. The LA theorem, or leg-acute, and LL theorem, or leg-leg, are useful shortcuts for proving congruence.

Congruency of Isosceles Triangles: Proving the Theorem

9. Congruency of Isosceles Triangles: Proving the Theorem

Isosceles triangles have two equal sides. Are the base angles also equal? In this lesson, we'll prove how this is true. We'll also prove the theorem's converse.

Midpoint Theorem: Definition & Application

10. Midpoint Theorem: Definition & Application

Postulates and proven theorems allow us to know and understand certain things about geometric figures. In this lesson, we will be learning about the Midpoint Theorem.

Proof by Contradiction: Definition & Examples

11. Proof by Contradiction: Definition & Examples

One of several different ways to prove a statement in mathematics is proof by contradiction. Learn the definition of this method and observe how it is applied to proving a statement's truth value through examples and exploration.

Properties of Right Triangles: Theorems & Proofs

12. Properties of Right Triangles: Theorems & Proofs

In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.

Special Right Triangles: Types and Properties

13. Special Right Triangles: Types and Properties

Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.

The Pythagorean Theorem: Practice and Application

14. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

The Pythagorean Theorem: Converse and Special Cases

15. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

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.

Other Chapters

Other chapters within the MTEL Mathematics (Elementary) (53): Practice & Study Guide course

Support