About This Chapter
TExES Math 4-8: Properties of Geometric Shapes - Chapter Summary
These lessons cover the essential properties of geometric shapes as part of your preparation for the TExES Math 4-8 exam. Use the videos and text transcripts to help you study the axiomatic system; Euclid's axiomatic geometry; and points, angles and lines in geometry. You'll also look at different types of angles and perpendicular, transverse and parallel lines. Once you finish this chapter, you should be prepared to do the following:
- Identify the properties of rectangles, rhombuses and squares
- Define the properties of triangles
- Find the perimeter and area of triangles and rectangles
- Use the Pythagorean Theorem
- Differentiate between area and circumference in circles
- Describe tessellations using symmetry
- Apply scale factors to area, perimeter and volume of similar figures
Our instructors guide you through each topic with animated and entertaining video lessons to prepare you for the test. Jump to tagged video sections to review specific concepts you need to master for the exam, and check out the video transcripts for offline study.
1. The Axiomatic System: Definition & Properties
Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.
2. Euclid's Axiomatic Geometry: Developments & Postulates
Learn how the way we do proofs in geometry had its start with Euclid in this video lesson. Learn about his contributions to the geometry we know today. Also learn about the five basic truths that he used as a basis for all other teachings.
3. Points, Lines & Angles in Geometry
After watching this video lesson, you should understand the basic terms that form the foundation of geometry. Learn what a point is, what a line is, what an angle is, and learn about a special type of angle called a right angle.
4. Types of Angles: Vertical, Corresponding, Alternate Interior & Others
In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.
5. Parallel, Perpendicular and Transverse Lines
What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.
6. Properties of Shapes: Rectangles, Squares and Rhombuses
What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.
7. Triangles: Definition and Properties
What makes a shape a triangle? In this lesson, we'll explore the definition of a triangle, then analyze the parts of triangles, including the vertices, base and height.
8. Perimeter of Triangles and Rectangles
Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.
9. Area of Triangles and Rectangles
How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.
10. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
11. Circles: Area and Circumference
Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.
12. Using Symmetry to Describe Tessellations
Tessellations are a very common way for geometric concepts to be applied in the real world. In this lesson, we'll look at how to use symmetry to help describe different types of tessellations.
13. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.
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Other chapters within the TExES Mathematics 4-8 Exam (115): Study Guide & Review course
- About the TExES Math 4-8 Exam
- TExES Math 4-8: Basic Arithmetic
- TExES Math 4-8: Number Theories & Computation Strategies
- TExES Math 4-8: Math Expressions & Formulas
- TExES Math 4-8: Decimals
- TExES Math 4-8: Fractions
- TExES Math 4-8: Percent Notation
- TExES Math 4-8: Calculations, Ratios & Proportions
- TExES Math 4-8: Real Numbers
- TExES Math 4-8: Sequences & Series
- TExES Math 4-8: Exponents & Exponential Expressions
- TExES Math 4-8: Exponentials & Logarithms
- TExES Math 4-8: Radical Expressions
- TExES Math 4-8: Algebraic Expressions & Equations
- TExES Math 4-8: Functions
- TExES Math 4-8: Trigonometric Functions & Graphs
- TExES Math 4-8: Graphing Piecewise Functions
- TExES Math 4-8: Absolute Value Equations
- TExES Math 4-8: Solving & Graphing Inequalities
- TExES Math 4-8: Imaginary & Complex Numbers
- TExES Math 4-8: Linear Equations
- TExES Math 4-8: Quadratic Equations
- TExES Math 4-8: Measurement & the Metric System
- TExES Math 4-8: Triangles, Theorems & Proofs
- TExES Math 4-8: Three-Dimensional Geometric Figures
- TExES Math 4-6: The Coordinate System
- TExES Math 4-8: Basic Geometric Constructions
- TExES Math 4-8: Summarizing Data
- TExES Math 4-8: Organizing & Displaying Data
- TExES Math 4-8: Mathematical Probability
- TExES Math 4-8: Mathematical Processes & Perspectives
- TExES Math 4-8: Mathematical Learning & Instruction
- TExES Math 4-8: Mathematical Assessments
- TExES Mathematics 4-8 Flashcards