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Ch 6: Honors Geometry: Similar & Congruent Triangle Proofs

About This Chapter

Similar and congruent triangle proofs are used to establish triangular relationships. This chapter of your Honors Geometry course looks at the ways proofs help you to work with triangles of varying measurements and traits.

Honors Geometry: Similar & Congruent Triangle Proofs - Chapter Summary and Learning Objectives

Triangles can be seen as similar just by looking at them, but using mathematically proven formulas will make your studies much easier. These lessons contain a number of proofs that verify similarity and congruence in triangles that will appear in your geometry problems and on graphs. Topics you'll look at include the following:

  • How to use the AAS Theorem
  • How to utilize the Perpendicular Bisector Theorem
  • What the Triangle Congruence Postulates are
  • How to prove relationships in congruence and similarity
  • What the properties are for concurrent triangle lines

VideoObjective
Triangle Proportionality TheoremUnderstand how to use this theorem to solve problems involving triangles.
How to Identify Similar TrianglesLearn to recognize triangle traits.
Applications of Similar TrianglesApply knowledge of similar triangles to solve problems.
Congruence Proofs: Corresponding Parts of Congruent TrianglesFind similar parts of triangles using congruence proofs.
The AAS (Angle-Angle-Side) Theorem: Proof and ExamplesUse the AAS Theorem to find congruency.
Perpendicular Bisector Theorem: Proof and ExampleSee how to divide lines into equal halves with this theorem.
Angle Bisector Theorem: Proof and ExampleStudy examples of this theorem and see how it works.
Triangle Congruence Postulates: SAS, ASA & SSSCompare the three postulates and find out how they each prove congruency.
The Transitive Property of Similar TrianglesDiscover how this property is used with similar triangles.
Congruence of Isosceles Triangles: Proving the TheoremLearn to prove this theorem as well as its converse.
Similarity Transformations in Corresponding FiguresTake a look at how to transform similar figures.
How to Prove Relationships in Figures using Congruence & SimilarityUse what you have learned to prove relationships geometrically.
Practice Proving Relationships using Congruence & SimilarityApply skills you've gained with practice problems.
Properties of Concurrent Lines in a TriangleReview terms related to concurrent lines.

14 Lessons in Chapter 6: Honors Geometry: Similar & Congruent Triangle Proofs
Test your knowledge with a 30-question chapter practice test
Triangle Proportionality Theorem

1. Triangle Proportionality Theorem

Watch this video lesson to learn all about the triangle proportionality theorem and how you can use this interesting theorem to help you solve problems. Learn how a parallel line can create sides that are proportional to each other.

How to Identify Similar Triangles

2. How to Identify Similar Triangles

Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.

Applications of Similar Triangles

3. 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.

Congruence Proofs: Corresponding Parts of Congruent Triangles

4. 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.

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.

Perpendicular Bisector Theorem: Proof and Example

6. 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

7. 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.

Triangle Congruence Postulates: SAS, ASA & SSS

8. 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.

The Transitive Property of Similar Triangles

9. The Transitive Property of Similar Triangles

Watch this video lesson and you will understand what the transitive property is and how it applies to similar triangles. Watch as we apply the transitive property to three similar triangles.

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.

Similarity Transformations in Corresponding Figures

11. 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

12. 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

13. 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.

Properties of Concurrent Lines in a Triangle

14. Properties of Concurrent Lines in a Triangle

Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.

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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