Ch 36: TExES Core Subjects 4-8: Triangles, Theorems & Proofs

About This Chapter

This chapter prepares you for content you'll encounter on the Texas Examinations of Educator Standards (TExES) Core Subjects 4-8 test. The subject matter covered in these lessons deals with triangles, theorems and proofs.

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

Our expert instructors have assembled this chapter so that you can brush up on topics relating to triangles, theorems and proofs. The lessons will help you answer TExES Core Subjects 4-8 test questions about:

  • Triangle congruence postulates
  • Explanation of converse of a statement
  • AAS, HA and HL theorems and proofs
  • Perpendicular bisector and angle bisector theorems and proofs
  • Congruence of right and isosceles triangles

These video lessons have a short, average run time of 5-10 minutes. After finishing a lesson, you can take a practice quiz or just go to the next lesson. You'll find helpful tools featured in the lessons, such as the Timeline, which makes it easy to find specific material in a video. You can ask instructors any questions that you have using either the Teacher tab or your Dashboard.

10 Lessons in Chapter 36: TExES Core Subjects 4-8: Triangles, 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.

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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