About This Chapter
Understanding Transformations in Math - Chapter Summary
The lessons in this chapter will teach you to analyze the properties of polygons and their components. You'll learn to use properties of points, lines, planes, angles, length and distances to solve problems. Rigid motions and the definition of congruence are covered, and this chapter will also explore symmetry in geometry.
You'll study transformations, such as reflections, translations, glide-reflections, dilations and rotations, and learn about their properties. Another lesson covers problem solving by using transformations and their compositions, and you'll get instruction on applying transformations in the coordinate plane. Reflectional, rotational and translational symmetry using transformation is part of this chapter as well. These lessons will give you a solid understanding of geometry topics that include:
- Geometry vocabulary and definitions of key terms
- How to shift graphs on a plane
- Rotations and reflections of quadrilaterals and regular polygons
- Definitions of rotation, reflection and translation
- Drawing transformed figures
- Identifying sequences of transformations that make one figure into another
- Transforming figures by using rigid motions
- Transformations in the coordinate plane
Experienced instructors will guide you through each topic in these concise, engaging video lessons, using examples from the real world to explain their points. Written transcripts of each lesson are available to give you another method to access this material. There is a short multiple-choice quiz at the end of each video lesson, with links back to video so you can review key passages and terms.
1. Transformations: How to Shift Graphs on a Plane
What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!
2. What is Translation in Math? - Definition, Examples, & Terms
In mathematics, translation refers to moving an object without changing it in any other way. This lesson will describe how to translate an object and give some examples. A quiz will follow to test your knowledge.
3. Reflections in Math: Definition & Overview
A reflection of an object is a 'flip' of that object across a line. This lesson will describe the basics of reflection, how to recognize one and how to create one.
4. How to Graph Reflections Across Axes, the Origin, and Line y=x
A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.
5. Glide Reflection in Geometry: Definition & Example
In this lesson, we will look at transformations of geometric figures and concentrate on one type of transformation in particular: a glide reflection. Through a definition and examples, we will become comfortable with this type of transformation.
6. Dilation in Math: Definition & Meaning
Dilations are transformations that change figures in specific ways. Learn about these changes and how to complete dilations here. Then test your understanding with a quiz.
7. Transformations in Math: Definition & Graph
In geometry, transformation refers to the movement of objects in the coordinate plane. This lesson will define and give examples of each of the four common transformations and end with a quiz to make sure you are moving in the right direction.
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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
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- 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