Ch 33: TACHS: Triangle Theorems & Proofs

About This Chapter

As your eighth-grade student prepares to pass the TACHS examination and enter a Catholic high school, they could benefit from this chapter on triangle theorems and proofs. Studying the lessons could sharpen their math skills prior to taking the entrance exam.

TACHS: Triangle Theorems and Proofs - Chapter Summary

This chapter is made up of video lessons that teach triangle theorems and proofs. Since the TACHS examination may include questions on congruent triangles, perpendicular bisectors, similar triangles and the converse of a statement, these lessons focus on these and related subjects. Your eighth-grade student could also learn to prove triangle theorems, write proportions and identify the congruence of triangles. With dedication and effort, your student might become proficient at:

  • Solving problems involving similar triangles
  • Using triangle congruence postulates
  • Applying the CPCTC (corresponding parts of congruent triangles are congruent) theorem
  • Understanding the converse of a statement and similarity transformations
  • Proving relationships
  • Practice using the AAS, HA, HL, angle bisector and perpendicular bisector theorems
  • Using the LL and LA theorems
  • Proving a theorem and its converse

Even as the TACHS examination testing date approaches, your student can learn at his or her own pace when they have access to a mobile device or a desktop computer. The online video lessons in this chapter are developed and presented by professionals who want to help your child succeed. The engaging lessons are animated, and they consist of playback and pause functions. Video tags permit them to skip ahead from one main topic to another. Text transcripts and self-assessment quizzes add to your student's educational experience.

TACHS: Triangle Theorems and Proofs Chapter Objectives

Students who make use of this chapter and its lessons on triangle theorems and proofs could properly address these kinds of questions on the TACHS examination. Consisting of questions that measure skills in mathematics, reading and language as well as reasoning abilities, the assessment is given on paper.

Students should bring along several pencils to the testing appointment. Calculators, cell phones and other electronic devices aren't permitted on the premises during testing. Testing takes two about hours, and there are no scheduled breaks. The examination is given in November, and scores should be received within a couple of months.

14 Lessons in Chapter 33: TACHS: 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.

How to Prove Relationships in Figures using Congruence & Similarity

6. How to Prove Relationships in Figures using Congruence & Similarity

In this lesson, we'll look at similar and congruent figures and the properties that they hold. We will then look at how to use these properties to prove relationships in these figures in various examples.

Practice Proving Relationships using Congruence & Similarity

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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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