Ch 36: NES Math: Triangle Theorems & Proofs

About This Chapter

Use our lessons to refresh your understanding of different types of triangle theorems and methods for proving them as you study for the NES Math test. The videos, quizzes and other tools in this study guide can support you in your test preparation.

NES Math: Triangle Theorems & Proofs - Chapter Summary

This chapter's lessons offer a review of theorems and proofs about triangles that will help you answer these types of questions on the NES Math test. Topics covered in these videos include:

  • Postulates of triangle congruence and congruence proofs
  • Definition of converse
  • How to prove relationships through congruence and similarity
  • The angle-angle-side, hypotenuse angle and hypotenuse leg theorems
  • The perpendicular bisector and angle bisector theorems
  • Congruency of right triangles
  • Proving congruency of isosceles triangles

Our instructors use humor and plenty of examples in lively lessons that you can watch anytime on a computer, smartphone or tablet. Short lesson quizzes let you assess your knowledge, and there's a clickable Timeline you can use to easily locate key passages in the video for review. You can track your progress through the Dashboard, a personalized tool that notes what lessons you've completed and may even suggest new courses that could help you.

NES Math: Triangle Theorems & Proofs Chapter Objectives

In Arizona, New Mexico, Oregon, Washington and Wisconsin, applicants for teaching certification in secondary-level math must pass the NES Math test. The test consists entirely of multiple-choice questions which require you to solve a problem or read a question and select the best answer from several choices. The quizzes in our lessons are in this format and can provide good practice in test-taking as well as letting you evaluate what you've learned.

The NES Math test questions are divided into five content domains, and questions from the Triangle Theorems & Proofs chapter are in the Measurement and Geometry content domain. This part of the test accounts for 19% of the total scoring.

11 Lessons in Chapter 36: NES Math: Triangle Theorems & Proofs
Test your knowledge with a 30-question chapter practice test
Triangle Congruence Postulates: SAS, ASA & SSS

1. 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

2. 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

3. 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.

Practice Proving Relationships using Congruence & Similarity

4. Practice Proving Relationships using Congruence & Similarity

In geometry, if two shapes are similar they have the same shape but different sizes, while two congruent shapes have the same shape and size. In this lesson, you will learn how to prove that shapes are similar or congruent.

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.

Perpendicular Bisector Theorem: Proof and Example

8. Perpendicular Bisector Theorem: Proof and Example

Perpendicular bisectors are multifunctional lines. They're not only perpendicular to the line in question, they also neatly divide it into two equal halves. In this lesson, we'll learn about the perpendicular bisector theorem.

Angle Bisector Theorem: Proof and Example

9. Angle Bisector Theorem: Proof and Example

The angle bisector theorem sounds almost too good to be true. In this lesson, we set out to prove the theorem and then look at a few examples of how it's used.

Congruency of Right Triangles: Definition of LA and LL Theorems

10. 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

11. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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