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Ch 25: TExES Math 4-8: Triangles, Theorems & Proofs

About This Chapter

This chapter's resources have been designed uniquely to help you get ready for the TExES Math 4-8 examination. These lessons on triangles, theorems and proofs might help you qualify to meet state certification standards.

TExES Math 4-8: Triangles, Theorems & Proofs - Chapter Summary

The lessons of this chapter can help you master everything you need to know about triangles, theorems and proofs. Our videos and text transcripts will cover the following topics as they are included on the exam:

  • Triangle congruence postulates and proofs
  • Key theorems in context, including: AAS (angle-angle-side), HA (hypotenuse angle), HL (hypotenuse leg), perpendicular bisectors, angle bisectors, LA (leg-acute) and LL (leg-leg) congruency of right triangles and congruency of isosceles triangles
  • Applying similar triangles
  • Explaining statement converses

Our qualified instructors will guide you through each topic to prepare you for the exam. Use our tagging system to jump to specific video sections and use the text transcripts to review the concepts you need to brush up on.

Objectives of the TExES Math 4-8: Triangles, Theorems & Proofs Chapter

The TExES Math 4-8 test assesses your total comprehension of mathematic concepts and strategies as well as your competency in teaching to determine whether you meet Texas state standards for mid-elementary level teacher licensing. This chapter's topics are part of the Geometry and Measurement domain, which makes up approximately 21% of the overall exam.

Use our accompanying self-check assessments to test your understanding of these crucial concepts while also familiarizing yourself with the types of questions you'll actually see on exam day. All of the questions on the TExES test are multiple-choice and are administered via computer.

11 Lessons in Chapter 25: TExES Math 4-8: Triangles, 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.

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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