# Ch 33: Praxis Middle School Math: Similarity & Congruence

### About This Chapter

## Praxis Middle School Math: Similarity & Congruence - Chapter Summary

Congruence and similarity require different methods of proof in triangles. This chapter of video lessons contained within the Praxis Middle School Math course provides a comprehensive study guide that will refresh your memory of the concepts before you take the Praxis Middle School Math exam. As you move through the video lessons, you will be looking at the following concepts:

- The triangle proportionality theorem
- Identifying similar triangles
- Congruence proofs
- Similarity transformations
- Proving relationships
- Construction and examples of similar polygons
- AA criterion and similarity theorem
- Math's golden ratio

This chapter is easy to take with you anywhere you go, as the video lessons are designed to be viewed on both mobile devices and computers. After you have finished, you can take the self-assessment quizzes included with each lesson to see how ready you are for the Praxis exam.

### 1. 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.

### 2. 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.

### 3. Congruence Proofs: Corresponding Parts of Congruent Triangles

Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.

### 4. Similarity Transformations in Corresponding Figures

Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.

### 5. How to Prove Relationships in Figures using Congruence & Similarity

In this lesson, we'll look at similar and congruent figures and the properties that they hold. We will then look at how to use these properties to prove relationships in these figures in various examples.

### 6. Practice Proving Relationships using Congruence & Similarity

In geometry, if two shapes are similar they have the same shape but different sizes, while two congruent shapes have the same shape and size. In this lesson, you will learn how to prove that shapes are similar or congruent.

### 7. 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.

### 8. 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.

### 9. AA Similarity Postulate & Theorem

The AA similarity postulate and theorem can be useful when dealing with similar triangles. In this lesson, we will examine this postulate, see how and why it works, and put it to use in various examples.

### 10. 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!

### 11. What is the Golden Ratio in Math? - Definition & Examples

Explore the golden ratio, a special number that has united mathematics, art, and nature. You will learn the definition of the golden ratio along with several different ways it can be represented and viewed in the world around you.

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### Other Chapters

Other chapters within the Praxis Middle School Mathematics (5169): Practice & Study Guide course

- Praxis Middle School Math: Number Basics
- Praxis Middle School Math: Rational Numbers
- Praxis Middle School Math: Properties of Numbers
- Praxis Middle School Math: Number Structure
- Praxis Middle School Math: Absolute Value
- Praxis Middle School Math: Equality
- Praxis Middle School Math: Arithmetic Operations
- Praxis Middle School Math: Introduction to Fractions
- Praxis Middle School Math: Operations with Fractions
- Praxis Middle School Math: Decimals
- Praxis Middle School Math: Percents
- Praxis Middle School Math: Ratios & Rate of Change
- Praxis Middle School Math: Proportional Relationships
- Praxis Middle School Math: Estimation
- Praxis Middle School Math: Scientific Notation & Exponents
- Praxis Middle School Math: Square Roots
- Praxis Middle School Math: Roots & Radicals
- Praxis Middle School Math: Algebra Basics
- Praxis Middle School Math: Principles of Algebra
- Praxis Middle School Math: Solving Word Problems
- Praxis Middle School Math: Functions
- Praxis Middle School Math: Linear Equations
- Praxis Middle School Math: Solving Linear Equations
- Praxis Middle School Math: Patterns in Math
- Praxis Middle School Math: Graphing Functions
- Praxis Middle School Math: Polynomials
- Praxis Middle School Math: Quadratic Equations
- Praxis Middle School Math: Systems of Equations
- Praxis Middle School Math: Area, Perimeter & Volume
- Praxis Middle School Math: Properties & Theorems
- Praxis Middle School Math: Parallel, Perpendicular & Intersecting Lines
- Praxis Middle School Math: Properties of Triangles
- Praxis Middle School Math: Quadrilaterals
- Praxis Middle School Math: Polygons
- Praxis Middle School Math: Circles
- Praxis Middle School Math: Coordinate Geometry
- Praxis Middle School Math: Measurement
- Praxis Middle School Math: Geometric Construction
- Praxis Middle School Math: Data
- Praxis Middle School Math: Line Graphs
- Praxis Middle School Math: Data Presentation
- Praxis Middle School Math: Probability
- Praxis Middle School Math: Counting Principles
- Praxis Middle School Math: Data Sets
- Praxis Middle School Math: Logic
- Praxis Middle School Math: Modeling
- Praxis Middle School Mathematics Flashcards