# Ch 44: NES Middle Grades Math: Similar Polygons

### About This Chapter

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

The National Evaluation Series (NES) Middle Grades Mathematics exam is certain to include questions of proportionality and relativity between polygons. This chapter will give you the tools you'll need to answer them. Here, we define similarity and provide theorems and proofs describing their properties and relationships. The topics of your review in this chapter include:

- Describing proportions and ratios
- Finding geometric mean
- Defining similar polygons and triangles
- Working with the transitive property and triangle proportionality
- Building similar polygons
- Understanding properties of right angles

Our comprehensive review and practice platform gives you the opportunity to get a quick dose of instruction from experienced math instructors and practice answering the kinds of multiple-choice questions you are likely to see on the real exam. We keep things fun and interesting in the lesson videos to ease the study pain and help provide you with tons of mnemonic cues. Print out the lesson transcripts and worksheets for additional study resources.

### NES Middle Grades Math: Similar Polygons Objectives

Taking the NES Middle Grades Mathematics exam will require you to answer 150 multiple-choice questions within a 4-hour, 15-minute time limit. The Measurements and Geometry content domain, which is where this content should principally fall, accounts for about 25% of the test content. The related objective is 'Objective 0008,' and it includes several Euclidean geometry topics.

Passing the exam requires a scaled score of 220 or higher. Your detailed score report will be published a couple of weeks after you take the test, but you will be able to receive your scaled score before leaving the testing center. Visit the NES website to complete registration, check testing and score reporting schedules, and download the complete breakdown of the NES Middle Grades Mathematics exam.

### 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 NES Middle Grades Mathematics (203): Practice & Study Guide course

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