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Ch 36: NMTA Math: Triangle Theorems & Proofs

About This Chapter

Watch these fun video lessons to review triangle theorems and proofs as part of your NMTA Math certification assessment preparation. If you have any trouble with the lesson material or get stuck on a quiz question, please send a question to our instructors for guidance.

NMTA Math: Triangle Theorems & Proofs - Chapter Summary

If you're preparing to take the NMTA Math certification assessment, watch these videos to study the triangle theorems and proofs you'll likely be tested on. Lesson topics include:

  • The SAS, ASA and SSS triangle congruence postulates
  • Congruence proofs and converse of a statement
  • Using congruence and similarity to prove relationships
  • The AAS, HA and HL theorems
  • The perpendicular bisector and angle bisector theorems
  • Congruency in right and isosceles triangles

Lesson quizzes let you practice working through the proofs and help you retain the information from the videos. Use the lesson transcripts to track down key ideas for additional review.

Objectives of the NMTA Math: Triangle Theorems & Proofs Chapter

Use the videos and quizzes in this chapter to master triangle proofs and theorems ahead of your NMTA Math certification assessment. The computer-administered exam includes 150 multiple-choice questions covering five content areas: calculus and trig; math processes and number sense; measurement and geometry; stats, probability and discrete math; and patterns, algebra and functions. The topics of this chapter can be found within the measurement and geometry section, which makes up 19% of the test questions. You'll be allowed four and a quarter hours to complete the assessment.

11 Lessons in Chapter 36: NMTA 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.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

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