Ch 25: FTCE Math: Similar & Congruent Triangle Proofs

About This Chapter

Get information on similar and congruent triangle proofs by studying this chapter. As you prepare for the FTCE Math exam, the video lessons and quizzes can familiarize you with and test you on the concepts you'll need to know.

FTCE Math: Similar & Congruent Triangle Proofs - Chapter Summary

This chapter on similar and congruent triangle proofs is designed to provide you with a convenient way of preparing for the FTCE Math exam. Learn at your own pace as you refresh your knowledge of:

  • The triangle proportionality, perpendicular bisector and angle bisector theorems
  • Similar triangles and triangle congruence postulates
  • The angle-angle-side theorem (AAS)
  • The transitive property
  • Isosceles triangles
  • Similarity transformations
  • Concurrent lines

The video lessons are taught by experienced educators who strive to make the learning process entertaining. Take the multiple-choice quizzes to test your comprehension. You can visit the dashboard if you'd like to submit your questions to our experts.

11 Lessons in Chapter 25: FTCE Math: 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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