# Ch 29: Honors Algebra 1: Similar Polygons

### About This Chapter

## Honors Algebra 1: Similar Polygons - Chapter Summary and Learning Objectives

These lessons were developed to teach you about similar polygons. Our expert instructors use a video format with lessons lasting 5-10 minutes. Each has a quiz to take at the end to assess your comprehension of what you just studied. If you need to restudy something in the lesson, you can refer to the lesson transcript, or you can use the video timeline tool to replay any specific segment. You can track your progress on your dashboard. At the end of these lessons, you should know:

- Ratios and proportions
- The geometric mean
- The Angle Bisector Theorem
- Similar polygons and triangles
- Properties of right triangles
- The Pythagorean Theorem

Lesson | Objective |
---|---|

Ratios and Proportions: Definition and Examples | Learn the relationship between ratios and proportions and how they are used in real life. |

Geometric Mean: Definition and Formula | Get to know how the geometric mean differs from the arithmetic mean and when it is preferred. |

Angle Bisector Theorem: Definition and Example | Learn the uses for the angle bisector. |

Solving Problems Involving Proportions: Definition and Examples | See how to use proportions to find missing sides. |

Similar Polygons: Definition and Examples | Analyze what makes two polygons similar to one another. |

The Transitive Property of Similar Triangles | Get familiar with similar triangles and how the transitive property applies to them. |

Triangle Proportionality Theorem | Work out how to solve problems with this theorem. |

Constructing Similar Polygons | Distinguish the two factors which must be included when constructing similar polygons. |

Properties of Right Triangles: Theorems & Proofs | Explore the properties of right triangles and how to use them for problem solving. |

The Pythagorean Theorem: Practice and Application | Discuss this famous theorem and its uses. |

The Pythagorean Theorem: Converse and Special Cases | Evaluate how the Pythagorean Theorem relates to the law of cosines and how its converse can help you identify right triangles. |

What is a Polygon? - Definition, Shapes & Angles | Find out what a polygon is and what it looks like. |

### 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. Geometric Mean: Definition and Formula

Watch this video lesson to learn how different the geometric mean is from the arithmetic mean, or average, that we are all so familiar with. Learn in what circumstance the geometric mean is preferred. Also, learn the formula and how to use it.

### 3. Angle Bisector Theorem: Definition and Example

Watch this video lesson and learn how you can use the angle bisector theorem to help you find the lengths of missing sides. Also learn how you can identify an angle bisector just by looking at the lengths of the sides of a triangle.

### 4. Solving Problems Involving Proportions: Definition and Examples

Learn how you can use proportions to find missing sides and how to increase or decrease the sizes of objects to create models of them in this video lesson.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. Constructing Similar Polygons

This lesson will teach you how to construct similar polygons, which are very useful in many quantitative fields. You'll learn that all of this has something to do with, of all things, snowflakes!

### 9. Properties of Right Triangles: Theorems & Proofs

In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.

### 10. 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.

### 11. 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.

### 12. What is a Polygon? - Definition, Shapes & Angles

Polygons are everywhere! In this lesson, you will learn what they are and what they look like. You will also learn about a special class of polygons and how to find its angles.

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### Other Chapters

Other chapters within the Honors Algebra 1 Textbook course

- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Properties of Real Numbers
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Solving Algebraic Expressions & Equations
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- Honors Algebra 1: Matrices in Linear Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Probability & Statistics
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Pre-Calculus Geometry
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math