# Ch 6: Big Ideas Math Geometry Chapter 6: Relationships Within Triangles

### About This Chapter

## How It Works:

- Identify the lessons within this chapter that corresponds to what you're studying in the Big Ideas Math Geometry chapter of your textbook.
- Watch fun videos that cover geometrical relationships within triangles that you need to learn or review.
- Complete the quiz after watching each video lesson 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:

- Perpendicular bisectors
- The angle bisector theorem
- Concurrent triangle lines
- The triangle midsegments theorem
- Indirect proof in geometry
- Inequality theorems
- Triangle inequality
- Triangles and the hinge theorem

*Big Ideas Math is a registered trademark of Big Ideas Learning LLC, which is not affiliated with Study.com.*

### 1. Perpendicular Bisector: Definition, Theorem & Equation

How can we draw a triangle that will have two exactly equal length sides? Or what if we need to find the center of a circle that passes through a given set of points? In this lesson, we'll learn about the perpendicular bisector and how useful it can be in geometry!

### 2. 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.

### 3. 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.

### 4. Proving the Triangle Midsegments Theorem

The Triangle Midsegment Theorem is extremely useful in real-world applications. This lesson will state the Triangle Midsegment Theorem, apply it to an example, and then provide a proof of the theorem.

### 5. Indirect Proof in Geometry: Definition & Examples

There are many different methods that can be used to prove a given theory. One of those methods is indirect proof. In this lesson, we will explore indirect proof and learn the steps taken to use this method to prove a given theory.

### 6. Theorems of Inequality

In this lesson, we will learn about the geometrical inequality relationships that exist between the sides and angles of a triangle, with the help of illustrative images.

### 7. Triangle Inequality: Theorem & Proofs

In this lesson, we will use definitions and proofs to learn what the triangle inequality theorem is, why it works, and how to use it to determine if three given line segments can form a triangle.

### 8. Comparing Triangles with the Hinge Theorem

The hinge theorem is a useful theorem in real-life applications. This lesson will define the hinge theorem and use it to compare triangles. We will also look at a real-life application of the hinge theorem.

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### Other Chapters

Other chapters within the Big Ideas Math Geometry: Online Textbook Help course

- Big Ideas Math Geometry Chapter 1: Basics of Geometry
- Big Ideas Math Geometry Chapter 2: Reasoning and Proofs
- Big Ideas Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Big Ideas Math Geometry Chapter 4: Transformations
- Big Ideas Math Geometry Chapter 5: Congruent Triangles
- Big Ideas Math Geometry Chapter 7: Quadrilaterals and Other Polygons
- Big Ideas Math Geometry Chapter 8: Similarity
- Big Ideas Math Geometry Chapter 9: Right Triangles and Trigonometry
- Big Ideas Math Geometry Chapter 10: Circles
- Big Ideas Math Geometry Chapter 11: Circumference, Area, and Volume
- Big Ideas Math Geometry Chapter 12: Probability