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 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.
2. Properties of Congruent and Similar Shapes
In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.
3. Triangle Congruence Postulates: SAS, ASA & SSS
When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.
4. Applications of Similar Triangles
Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.
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.
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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
- 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