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Ch 36: MTLE Mathematics: Similar & Congruent Triangle Proofs

About This Chapter

This chapter covers the information about similar and congruent triangle proofs that you should review before taking the MTLE mathematics exam. The lessons and quizzes will allow you to practice using these proofs.

MTLE Mathematics: Similar & Congruent Triangle Proofs - Chapter Summary

Get ready for the MTLE mathematics exam by brushing up on what you know about triangle proofs. The lessons in this chapter were created to help you review:

  • The triangle proportionality theorem
  • Steps for identifying and using similar triangles
  • Differentiating between the triangle congruence postulates
  • The AAS, perpendicular bisector and angle bisector theorems
  • Applications of the transitive property and properties of concurrent lines
  • How to prove the congruency of isosceles triangles
  • The use of similarity transformations

These video lessons guide you step by step through the triangle proofs. If you need extra review, you can read the lesson transcripts for another chance to go over this topic.

11 Lessons in Chapter 36: MTLE Mathematics: 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.

Triangle Congruence Postulates: SAS, ASA & SSS

4. 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 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.

The Transitive Property of Similar Triangles

8. 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

9. 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

10. 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.

Properties of Concurrent Lines in a Triangle

11. 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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