# Ch 44: ORELA Middle Grades Math: Similar Polygons

### About This Chapter

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

Prepare for questions on similar polygons on the ORELA Middle Grades Math exam by watching the video lessons in this chapter. You can see the definition and examples of various polygons as well as review how to solve problems with proportions. The lessons cover:

- Ratios and proportions
- Geometric mean
- Problem solving with proportions
- Examples of similar polygons
- Similar triangles
- The transitive property
- Proportionality theorems
- Right triangles

These video lessons are led by expert instructors who use illustrations and fun examples to demonstrate these math concepts. You can also use the video transcripts, multiple-choice quizzes and end-of-chapter test to prepare for test day.

### ORELA Middle Grades Math: Similar Polygons Objectives

The ORELA Middle Grades Math exam is a 150-question multiple-choice test that includes questions in numbers and operations, algebra, geometry, measurement, statistics and discrete math. The topics covered in this chapter are part of the measurement and geometry section, which comprises 25% of the exam.

This computer-based exam is designed for prospective teachers who want to earn a credential to teach middle school math in Oregon. Take the chapter test and multiple-choice quizzes to get practice in answering the kinds of questions you could see when taking the Middle Grades Math test. These quizzes also let you test your knowledge of solving problems related to the properties similar polygons.

### 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.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the ORELA Middle Grades Mathematics: Practice & Study Guide course

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