# Ch 11: Amsco Geometry Chapter 12: Ratio, Proportion, and Similarity

### About This Chapter

## How it works:

- Identify the lessons in the Amsco Geometry Ratio, Proportion and Similarity chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the ratio, proportion and similarity 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 about:

- Proportions of line segments
- Similar polygons and triangles
- Dilations
- Concurrency of angle and perpendicular bisectors
- Concurrency of medians of triangles
- Proportions in right triangles
- The Pythagorean Theorem

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### 1. Ratios and Proportions: Definition and Examples

Watch this video lesson to learn how ratios and proportions are related. Also, learn how ratios and proportions are used in real life and how you can apply them to yours.

### 2. Proportion: Definition, Application & Examples

When we want to compare one ratio, or fraction, to another equivalent ratio, it's a proportion. Learn all about proportions and practice solving proportion problems in this lesson.

### 3. Similar Polygons: Definition and Examples

Watch this video to learn what makes two polygons similar to each other. You'll also learn the one distinguishing aspect of similar polygons and see an example of how to compare two polygons.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

### 8. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

### 9. Distance Formulas: Calculations & Examples

Let's go on a road trip! In this lesson, we'll practice calculations involving distance, rate and time. We'll also look at how we determine the relationship between distance and fuel.

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### Other Chapters

Other chapters within the Amsco Geometry: Online Textbook Help course

- Amsco Geometry Chapter 1: Essentials of Geometry
- Amsco Geometry Chapter 2: Logic
- Amsco Geometry Chapter 3: Proving Statements in Geometry
- Amsco Geometry Chapter 4: Congruence of Line Segments, Angles, and Triangles
- Amsco Geometry Chapter 5: Congruence Based on Triangles
- Amsco Geometry Chapter 6: Transformations and the Coordinate Plane
- Amsco Geometry Chapter 8: Slopes and Equations of Lines
- Amsco Geometry Chapter 9: Parallel Lines
- Amsco Geometry Chapter 10: Quadrilaterals
- Amsco Geometry Chapter 11: Geometry of Three Dimensions
- Amsco Geometry Chapter 13: Geometry of a Circle
- Amsco Geometry Chapter 14: Locus and Construction