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Ch 4: Discovering Geometry Chapter 4: Discovering and Proving Triangle Properties

About This Chapter

The Discovering and Proving Triangle Properties chapter of this Discovering Geometry Companion Course aligns with the same chapter in the Discovering Geometry textbook. These simple and fun video lessons are about five minutes long and help you learn the essential lessons about properties of triangles, including key theorems and postulates such as the AAS theorem. DISCOVERING GEOMETRY is a registered trademark of Angela H. Snead. Study.com has no affiliation with and is not endorsed by Angela H. Snead, by Michael Serra, the author and copyright holder of Discovering Geometry: An Investigative Approach; or by Kendall Hunt Publishing, the textbook's publisher.

How it works:

  • Identify the lessons in your textbook chapter with which you need help.
  • Find the corresponding video lessons within this online chapter.
  • Watch fun videos that cover the discovering and proving triangle properties topics you need to learn or review.
  • Complete the quizzes to test your understanding.
  • If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

Students will learn:

  • Fundamentals of math transformations
  • How to determine symmetry on the x-axis and y-axis
  • Ways to shift graphs on a plane
  • How to understand multiple transformations
  • Regular and semi-regular tessellations
  • Tessellations with non-regular polygons

8 Lessons in Chapter 4: Discovering Geometry Chapter 4: Discovering and Proving Triangle Properties
Measuring the Angles of Triangles: 180 Degrees

1. Measuring the Angles of Triangles: 180 Degrees

Watch this video lesson to see why a triangle's angles always add up to 180 degrees. Also, learn how you can use this unique fact about triangles to find an unknown angle in a triangle.

Congruency of Isosceles Triangles: Proving the Theorem

2. 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.

Interior and Exterior Angles of Triangles: Definition & Examples

3. Interior and Exterior Angles of Triangles: Definition & Examples

Knowing just a few things about the interior or exterior angles of triangles is sometimes all you need to put all the pieces together. Find out more in this lesson.

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.

Congruence Proofs: Corresponding Parts of Congruent Triangles

6. 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.

Direct Proofs: Definition and Applications

7. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

Angle Bisector Theorem: Proof and Example

8. 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.

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