About This Chapter
Properties of Shapes Overview - Chapter Summary
This chapter is filled with engaging lessons that make learning about the properties of shapes fun. Review these lessons at your own pace to get a quality overview of shapes like triangles and circles along with their properties. Review definitions and examples to ensure you fully comprehend this chapter. When finished, you will be ready to:
- Use sides and angles when classifying triangles
- Identify properties of right triangles and special right triangles
- Define and utilize the Pythagorean theorem
- Describe properties of circles, rectangles, squares, quadrilaterals, parallelograms and much more
- Find the area, circumference, diameter and radius of a circle
- Demonstrate knowledge of arc lengths
Access these lessons from any computer, smartphone or tablet when most convenient for your busy schedule. Review them in any sequence and as often as needed until you fully comprehend the properties of various shapes. Gauge your knowledge of this subject area by taking short lesson quizzes and a chapter exam. Any questions you have about lesson topics can be submitted to our experts.
1. Classifying Triangles by Angles and Sides
Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.
2. Properties of Right Triangles: Theorems & Proofs
In this lesson, you will learn about the properties of and theorems associated with right triangles, which have a wide range of applications in math and science. Specifically, we will discuss and prove the Pythagorean theorem and the right triangle altitude theorem. Let's get started.
3. Special Right Triangles: Types and Properties
Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.
4. Pythagorean Theorem: Definition & Example
Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.
5. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons
Four-sided objects are more than just squares and rectangles. In this lesson, we'll discuss quadrilaterals, parallelograms and trapezoids. We'll also discuss polygons, objects that can have more sides than you can count.
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. Properties of Shapes: Circles
Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.
8. 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.
9. How to Find the Diameter of a Circle: Definition, Formula & Example
Learn the definition of the diameter of a circle and how to find it using a simple formula. See some examples, then test your knowledge with a short quiz.
10. How to Find the Radius of a Circle: Definition & Formula
In this lesson, you will discover the definition of a radius. You will also learn how to find the radius of a circle using three different formulas based on diameter, circumference, and area.
11. Arc Length of a Sector: Definition and Area
In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths.
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Other chapters within the Pennsylvania Grades 4-8 - Math Subject Concentration (5158): Practice & Study Guide course
- Real & Rational Numbers
- Exponents & Operations
- Properties of Operations
- Fractions, Decimals & Percents
- Ratios, Rates & Proportional Relationships
- Number Theory & Estimation
- Radical & Exponential Expressions
- Linear Equations & Inequalities
- Nonlinear Equations & Inequalities
- Systems of Equations
- Sequences & Patterns in Math
- Understanding & Comparing Functions
- Function Graphs & Models
- Perimeter, Area & Volume Overview
- Properties of Angles & Lines
- Geometric Relationships & Transformations
- Systems of Measurement & Conversion
- Geometric Construction
- Data Interpretation in Math
- Dispersion & Probability Models
- Logical Reasoning & Visual Representations of Data
- Pennsylvania Grades 4-8 - Math Subject Concentration (5158) Flashcards