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Ch 44: 6th-8th Grade Geometry: Triangle Theorems & Proofs

About This Chapter

The video lessons in this chapter help 6th-8th graders improve their knowledge of triangle theorems and their ability to prove them. Students take multiple-choice lesson quizzes and a chapter exam to see how well they've grasped these geometry concepts.

6th-8th Grade Geometry: Triangle Theorems & Proofs - Chapter Summary

Your middle schooler can use this geometry chapter to reinforce what he or she has learned about triangle theorems and proofs at school. By watching the short video lessons, students are able to review key concepts and apply them to practice problems. Instructors cover the SAS, ASA and SSS postulates as well as the CPCTC theorem, among others. The lessons also explain how to verify the converse of conditional statements. Your 6th, 7th or 8th grader can get extra help by submitting questions to instructors and reviewing the lessons' transcripts. Students apply what they've learned in the videos to the problems in the self-assessment quizzes and chapter exam.

Chapter Lessons and Objectives

LessonObjective
Applications of Similar TrianglesStudents learn how to solve real-world problems involving similar triangles.
Triangle Congruence Postulates: SAS, ASA & SSSThe instructor teaches students to use the SAS, ASA and SSS postulates to determine if triangles are congruent.
Congruence Proofs: Corresponding Parts of Congruent TrianglesStudents practice solving problems using the CPCTC theorem.
Converse of a Statement: Explanation and ExampleThis lesson discusses the importance of verifying that the converse of a conditional statement is true.
Similarity Transformations in Corresponding FiguresStudents use examples to determine if two figures are similar based on similarity transformations.
How to Prove Relationships in Figures using Congruence & SimilarityIn this lesson, students learn to use similarity and congruence criteria to prove geometric figures' relationships.
Practice Proving Relationships using Congruence & SimilarityStudents apply what they learned in the previous lesson about proving relationships by completing practice problems.
The AAS (Angle-Angle-Side) Theorem: Proof and ExamplesThe instructor defines the AAS theorem and uses examples to demonstrate it.
The HA (Hypotenuse Angle) Theorem: Proof, Explanation & ExamplesThis lesson teaches students to use the HA theorem to verify that two right triangles are congruent.
The HL (Hypotenuse Leg) Theorem: Definition, Proof & ExamplesStudents solve practice problems using the HL theorem.
Perpendicular Bisector Theorem: Proof and ExampleThe instructor guides students through proving the perpendicular bisector theorem.
Angle Bisector Theorem: Proof and ExampleThis lesson explains the angle bisector theorem and illustrates it using examples.
Congruency of Right Triangles: Definition of LA and LL TheoremsStudents learn to use the LA and LL theorems for determining right triangles' congruency.
Congruency of Isosceles Triangles: Proving the TheoremWith this lesson, students learn to prove the congruency of isosceles triangles theorem and its converse.

14 Lessons in Chapter 44: 6th-8th Grade Geometry: Triangle Theorems & Proofs
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.

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Other Chapters

Other chapters within the 6th-8th Grade Math: Practice & Review course

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