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Ch 42: NMTA Middle Grades Math: Triangle Theorems & Proofs

About This Chapter

In New Mexico, the NMTA Middle Grades Mathematics test has been replaced by the NES Middle Grades Mathematics test. Use the video lessons in this chapter to refresh your comprehension of triangle theorems and proofs as you prepare to take the NES Middle Grades Mathematics test.

NMTA Middle Grades Math: Triangle Theorems & Proofs - Chapter Summary

The NES Middle Grades Mathematics test covers a variety of mathematical concepts, including triangle theorems and proofs. The video lessons in this chapter are designed to help you answer questions on the test that address the following:

  • Applications of similar triangles
  • Triangle congruence postulates
  • Congruence proofs
  • Converse of a statement
  • Proving relationships using congruence and similarity
  • The AAS, HA and HL theorems
  • Congruency of right triangles

The video lessons present detailed guidance in an entertaining package, making the learning process both comprehensive and fun. You can benefit from video transcripts if you learn best by reading and listening. Timelines are also available if you need to revisit specific topics within the videos.

NMTA Middle Grades Math: Triangle Theorems & Proofs Chapter Objectives

Use this NMTA Middle Grades Math: Triangle Theorems & Proofs chapter to learn the definitions and functions necessary to succeed on the NES Middle Grades Mathematics test. The topics covered in this chapter are found in the measurement and geometry section of the test, which constitutes about 25% of the total exam. Thoroughly explore the video lessons to prepare as much as possible and use the self-assessment quizzes to practice answering questions similar to those found on the exam.

All of the questions on the test are multiple choice and usually take the form of short paragraphs, sentences or questions. Each question is followed by four answers, one of which you will be required to choose as the best response to the question posed.

13 Lessons in Chapter 42: NMTA Middle Grades Math: Triangle Theorems & Proofs
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.

Similarity Transformations in Corresponding Figures

5. Similarity Transformations in Corresponding Figures

Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.

Practice Proving Relationships using Congruence & Similarity

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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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Other Chapters

Other chapters within the NMTA Middle Grades Mathematics (203): Practice & Study Guide course

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