# Ch 42: GACE Middle Grades Math: Similar Polygons

### About This Chapter

## GACE Middle Grades Math: Similar Polygons - Chapter Summary

In this chapter, our professional instructors prepare you for questions on similar polygons that are on the GACE Middle Grades Mathematics assessment. Watch the fun video lessons and you'll be able to do the following come test day:

- Understand ratios and proportions
- Find the geometric mean
- Solve problems with proportions
- Give examples of and construct similar polygons
- Identify similar triangles based on the AA criterion
- Explain the transitive property of similar triangles
- Define the triangle proportionality theorem
- Recognize the properties of right triangles

If you've got roughly 10 minutes or less, then you've got time to watch our videos. Our lessons contain step-by-step explanations, examples and graphics to improve your understanding of similar polygons. Be sure to also check out our video transcripts and take the self-assessment lesson quizzes.

### 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. 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.

### 4. 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.

### 5. Similar Triangles & the AA Criterion

This video lesson explains the AA criterion and shows you why you only need two corresponding angles to be equal for two triangles to be similar. You will also see how you can use it to help you identify similar triangles.

### 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.

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### Other Chapters

Other chapters within the GACE Middle Grades Mathematics (013): Practice & Study Guide course

- GACE Middle Grades Math: Basic Arithmetic Operations
- GACE Middle Grades Math: Solving Math Word Problems
- GACE Middle Grades Math: Properties of Numbers
- GACE Middle Grades Math: Roots & Radical Expressions
- GACE Middle Grades Math: Exponents & Exponential Expressions
- GACE Middle Grades Math: Scientific Notation
- GACE Middle Grades Math: Simplifying Expressions
- GACE Middle Grades Math: Integers
- GACE Middle Grades Math: Rational Numbers
- GACE Middle Grades Math: Introduction to Fractions
- GACE Middle Grades Math: Operations with Fractions
- GACE Middle Grades Math: Introduction to Decimals
- GACE Middle Grades Math: Operations with Decimals
- GACE Middle Grades Math: Percents
- GACE Middle Grades Math: Rates, Ratios & Proportions
- GACE Middle Grades Math: Number Theory
- GACE Middle Grades Math: Factoring
- GACE Middle Grades Math: Estimating & Rounding
- GACE Middle Grades Math: Monomials & Polynomials
- GACE Middle Grades Math: Writing Algebraic Expressions
- GACE Middle Grades Math: Basic Algebraic Expressions
- GACE Middle Grades Math: Algebraic Distribution
- GACE Middle Grades Math: One-Step Equations
- GACE Middle Grades Math: Two-Step Equations
- GACE Middle Grades Math: Rational Expressions
- GACE Middle Grades Math: The Coordinate Graph
- GACE Middle Grades Math: Linear Equations
- GACE Middle Grades Math: Systems of Linear Equations
- GACE Middle Grades Math: Negative Numbers
- GACE Middle Grades Math: Absolute Value
- GACE Middle Grades Math: Inequalities
- GACE Middle Grades Math: Number Patterns & Sequences
- GACE Middle Grades Math: Properties of Functions
- GACE Middle Grades Math: Graphing Functions
- GACE Middle Grades Math: Perimeter & Area
- GACE Middle Grades Math: Polyhedrons & Geometric Solids
- GACE Middle Grades Math: Symmetry, Similarity & Congruence
- GACE Middle Grades Math: Properties of Lines
- GACE Middle Grades Math: Angles
- GACE Middle Grades Math: Triangles
- GACE Middle Grades Math: Triangle Theorems & Proofs
- GACE Middle Grades Math: The Pythagorean Theorem
- GACE Middle Grades Math: Quadrilaterals
- GACE Middle Grades Math: Circles
- GACE Middle Grades Math: Circular Arcs & Measurement
- GACE Middle Grades Math: Transformations
- GACE Middle Grades Math: Measurement
- GACE Middle Grades Math: Data & Graphs
- GACE Middle Grades Math: Sets
- GACE Middle Grades Math: Statistics
- GACE Middle Grades Math: Data Collection
- GACE Middle Grades Math: Samples & Populations
- GACE Middle Grades Math: Probability
- GACE Middle Grades Mathematics Flashcards