Back To Course

CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, you will learn what prisms are and what makes rectangular prisms unique. There are several rules that identify a three-dimensional shape as a prism. You will also consider a few everyday items as examples of rectangular prisms.

Prisms are a certain kind of shape, but what makes them stand out? A **prism** is two polygons, or multiple-sided closed shapes, joined together to form an enclosed three-dimensional shape. For example, a box is a prism because it consists of two squares or rectangles joined together to make the enclosed three-dimensional figure seen here:

Two-dimensional shapes make the flat top and bottom sides, or **faces**, of a prism.

So any box, stacks of Post-It Notes, and even legal pads are all prisms because they're three-dimensional objects with congruent polygons as faces.

There are five rules for identifying a prism:

__Rule 1:__ is that the faces of a prism must be polygons. So even though it may seem that cylinders would be prisms, they don't fit the definition. This is because their faces are circles or ovals, which don't have sides and are therefore not polygons. So a can isn't a prism. No sides, no polygons, no prism.

A prism can have triangles as faces.

__Rule 2:__ states that the sides of a prism must be parallelograms. Parallelograms are quadrilaterals whose opposite sides are parallel. Consider a box and a triangular prism, all of their sides are parallelograms.

__Rule 3:__ The third rule says a prism's faces must be parallel. If one face lies at an angle to the other, they will at some point intersect, and the figure is not a prism. Also, if the faces aren't parallel, the sides won't be parallelograms.

In this figure, for example, the rear face lies at an angle compared to the front face. As a result, two of the sides are not parallelograms. Non-parallel faces create sides that are not parallelograms.

__Rule 4:__ states that the bases must be congruent. **Congruent** means the exact same shape and size.

A figure that has differently shaped faces creates sides that are not parallelograms. Since the faces are not congruent, this figure isn't a prism.

__Rule 5:__ Lastly, rule five says if a cross-section is taken of a prism parallel to its faces, the cross-section would be congruent with the prism's faces. This happens because the faces are congruent and parallel. This is true no matter where you slice it.

Think of it like a loaf of bread. If it's sliced parallel to the ends, no matter where you cut, the slices will have the same shape.

With all these rules, it's important to realize that there is something that isn't a rule. The angles between the sides and the faces do not have to be right angles. An **oblique prism** has slanted sides, but the faces are still congruent and parallel.

Although this type of prism's sides slant, its pentagonal faces are congruent and parallel and its sides are still parallelograms.

So where does all this get us with regard to rectangular prisms? Since there are many different shapes that can serve as faces, there are many different types of prisms. In fact, prisms are named for the shape of their faces. So a **rectangular prism** is simply a prism that has rectangles as its faces. It's an enclosed three-dimensional shape, but it's based on two rectangles. There are many common items that are in fact rectangular prisms.

This jewelry box is a three-dimensional object with a rectangular top and bottom. That makes it a rectangular prism!

In the same way, a mattress is a rectangular prism.

A mattress has a rectangular top and bottom. The congruent and parallel rectangular faces make it a rectangular prism.

And one more example:

This book stands on narrow rectangles. But it's still a three-dimensional figure based on two rectangles, so it is a rectangular prism.

A **prism** is two polygons joined together to form an enclosed three-dimensional shape. The rules that define a prism state that the faces must be polygons, the sides must be parallelograms, and the faces must be parallel. A three-dimensional shape that is a prism also must have faces that are congruent and cross-sections parallel to the faces must be congruent to the faces. Cylinders are not prisms because of a circular top and bottom.

**Oblique prisms** have slanted sides but are prisms because they have parallel and congruent faces. A **rectangular prism** is simply a prism with rectangular faces. Because a rectangular prisms faces must be rectangles, at least two of its sides will always be rectangles, even if the rest of its sides are squares.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
7 in chapter 16 of the course:

Back To Course

CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

- Properties of Shapes: Rectangles, Squares and Rhombuses 5:46
- Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons 6:42
- Properties of Shapes: Triangles 5:09
- Properties of Shapes: Circles 4:45
- Orthographic Projection: Definition & Examples 4:01
- The Golden Rectangle: Definition, Formula & Examples 6:12
- What is a Rectangular Prism? - Definition & Examples 4:31
- Go to CAHSEE - Properties of Shapes: Tutoring Solution

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Algorithmic Analysis, Sorting & Searching
- Computer Programming Basics
- Stacks & Queues for Data Structures
- Functions & Modules in Programming
- Built-In Data Types for Programming
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- The Lion of the Tribe of Judah: Symbol & Meaning
- Partial Fractions: Rules, Formula & Examples
- Risk Identification: Process & Analysis
- Design Constraints in Engineering: Definition & Example
- Filter Function in R Programming
- What is a VLAN? - Definition, Function & Implementation
- Room 101 Lesson Plan
- Quiz & Worksheet - Difference Between Temple & Synagogue
- Quiz & Worksheet - Dorsiflexion vs. Plantar Flexion
- Quiz & Worksheet - Narrative of the Life of Frederick Douglass
- Quiz & Worksheet - A Midsummer Night's Dream Play Within a Play
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- ESL Activities, Vocabulary & Writing Prompts
- Elementary Science Worksheets and Printables

- OSAT Reading Specialist (CEOE) (015): Practice & Study Guide
- Building & Launching a Successful Team
- Introduction to Sociology Textbook
- Major Events in World History Study Guide
- Basic Business Law Concepts
- GACE Middle Grades Math: Integers
- The Economics of Public Policies
- Quiz & Worksheet - Statutes in Law
- Quiz & Worksheet - Inverse Operations in Math
- Quiz & Worksheet - What Is Administrative Law?
- Quiz & Worksheet - Graham v. Connor
- Quiz & Worksheet - Horizontal Asymptotes

- Social Security: Legislation and Issues
- Irreducible Quadratic Factors: Definition & Graphical Significance
- English Language Learning Programs in California
- French Revolution Lesson Plan
- 504 Plans in Wisconsin
- SBEC Technology Application Standards for Teachers
- Florida State Standards for Language Arts
- NGSS Life Science for Middle School
- Sequence of Events Lesson Plan
- What Are Good SAT Scores?
- Andrew Jackson Lesson Plan
- Texas Teacher Evaluation System

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject