# Ch 27: Congruence and Similarity

### About This Chapter

## Congruence and Similarity - Chapter Summary

The video lessons in this chapter will show you about the properties of congruent and similar shapes. You'll learn to use the properties of congruence and similarity to explore geometric relationships, justify conjectures and prove theorems. Solving problems by using the properties of points, lines, planes, angles, lengths and distances are covered in these videos.

Another lesson uses geometric patterns and properties to make generalizations about two- and three-dimensional shapes, such as the relationships of sides and angles. You'll learn methods to determine if triangles are congruent. After watching all the videos in this chapter, you should have knowledge of these topics:

- Properties of dilations
- How to identify similar triangles
- Properties of congruent and similar shapes
- Similarity transformations
- Similar triangles and the AA Criterion
- Applications of similar triangles
- Proving similarity theorems about triangles
- Proving relationships in figures using congruence and similarity

You'll learn from experienced instructors who use examples from the real world to explain their points. Practice lessons allow you to hone your skills in problem solving. Every lesson contains a multiple-choice quiz so you can test your knowledge. The questions are linked back to the video, making it simple to review key passages and terms. The lessons are accompanied by a written transcript that also contains links to the video.

### 1. How to Identify Similar Triangles

Similar triangles are defined as two triangles that possess proportional corresponding sides and congruent corresponding angles. Triangle similarity theorems use angle and side comparisons to determine whether two triangles are similar. Learn about the language of similarity, triangle similarity theorems (Angle-Angle, Side-Angle-Side, & Side-Side-Side), and how to use theorems to identify similar triangles.

### 2. Properties of Congruent and Similar Shapes

When two shapes share the same size and form, they are congruent, and when they have the same form, but not necessarily the same size, they are similar. Learn how to compare shapes, explore the properties of congruent and similar shapes, and practice finding the lengths of sides and calculate the missing angles for both congruent and similar shapes.

### 3. Triangle Congruence Postulates: SAS, ASA & SSS

Triangle congruence postulates of side-side-side (SSS), side-angle side (SAS), or angle-side-angle (ASA) refer to truths about triangles without the need for proof. Explore the SSS, SAS, and ASA triangle congruence postulates in detail and learn how to apply them with provided examples.

### 4. Applications of Similar Triangles

Similar triangles have the same shape but differ in size. Learn about the applications of similar triangles, including how to use them and how to solve real-world problems with similar triangles.

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

Proving the relationship of figures through congruence uses properties of sides and angles. On the other hand, similarity can be used to prove a relationship through angles and sides of the figure. Learn more of these properties through the examples provided.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards