Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Isosceles, equilateral and obtuse, oh my! These are terms for triangles. But, what do they mean? In this lesson, we'll explore the properties of triangles and take a closer look at the different types of triangles you may encounter.

Triangles - they're the three-sided shape you see everywhere you look. They're the symbol for play and the sign to slow down. They're the ears on a cat and a slice of pizza. They're the gateway to the unknown and the monument to a long-ago empire.

They're even the musical instrument calling us to dinner if we live on a 19th century farm. Though I don't know how you're watching this online video from a 19th century farm. Let's take a closer look at the many facets of this seemingly simple shape.

First, let's define what we're talking about. A **triangle** is a polygon with three sides and three angles. You can remember that triangles have three sides and angles by that 'tri' in the name. 'Tri' means 'three,' whether you're talking about geometry, tricycles or triceratops.

In a triangle, the interior angles always add up to 180 degrees. So, in the triangle below, if one angle is 60 and another is 60, which is 120 total, then the other one has to be 180 - 120, which is also 60. If you ever know two angles of a triangle, you can always find the third by remembering the 180-degree rule.

Triangles that have particular properties get their own names. For example, this one:

Notice that all the angles are the same. As you might guess, there's a direct correlation between the angles and sides. When the angles are all the same, so are the sides. So, this is an example of an **equilateral triangle**, which is a triangle with three equal sides and three equal angles. Do you hear 'equal' in 'equilateral'? The term literally means 'equal sides.'

Some triangles only have two equal sides. A triangle with two equal sides and two equal angles is called an **isosceles triangle**. I think of isosceles triangles as an equilateral triangle's younger sibling. Its equalness is not as complete. Note below that the equal sides are always opposite the equal angles. So, if the angles on the bottom are equal, the sides with blue arrows are equal.

Then there's the awkward cousin to equilateral and isosceles triangles: the scalene triangle. A **scalene triangle** is a triangle with no equal sides or angles. Scalene means unequal, but it doesn't sound like unequal. It sounds like 'scale.' Think about yourself on a scale. If you're like me, you probably don't weigh exactly what you'd like to weigh. You're a bit (or more than a bit) off. And, scalene triangles are out of balance, too. None of their sides match.

We just compared triangles by their sides and angles, but we also classify triangles by just their angles. For example, a triangle with a right angle, which is a 90-degree angle, is called a **right triangle**. That makes sense, right? Right angle - right triangle.

But, what if you have a triangle with all angles less than 90 degrees? That's an **acute triangle**. The opposite of this is a triangle with an angle that's more than 90 degrees. That's an **obtuse triangle**. You may know that an angle less than 90 degrees is acute and an angle more than 90 degrees is obtuse. That's where these triangle names originate. You can also think of it this way: Acute means 'sharp or pointed.' Think of an acute pain. Or, forget the Latin derivation and just think of what makes 'a cute' triangle. Small angles!

Conversely, obtuse means 'dull or blunt.' Let's imagine we're early humans making arrowheads to kill some woolly mammoths. If your arrowhead looks like the one below - acute triangles - you might feast on mammoth steaks tonight. Mmm, gamey.

If they look like this one below - obtuse - they're duller, less pointy, and that mammoth may feast on you. Mmm, trampled to death.

These names for triangles are not mutually exclusive. For example, an equilateral triangle is necessarily an acute triangle. Think about that. All equilateral triangle angles are 60 degrees, so they're all less than 90 degrees. Also, you can have an isosceles triangle that's also a right triangle.

If one angle is 90 degrees and it's an isosceles triangle, the other angles must add up to 90, so they're each 45 degrees. Scalene triangles can be acute, obtuse or right triangles. That seems fitting since most people feel out of balance on a scale.

In summary, we learned about **triangles**, which are polygons with three sides and three angles. We looked at three main types of triangles. First, **equilateral triangles** are triangles with three equal sides and angles. Second, **isosceles triangles** are triangles with two equal sides and angles. Third, the awkward cousin, **scalene triangles**, which are triangles with no equal sides or angles.

Then we looked at the angles of triangles. There are **right triangles**, or triangles with one right angle. Then there are **acute triangles**, where all angles are less than 90 degrees, and **obtuse triangles**, where one angle is more than 90 degrees. Now I think I hear a triangle being played. It must be time for a 19th century farm dinner.

After reviewing this lesson, you'll have the ability to:

- Describe the properties of equilateral, isosceles and scalene triangles
- Identify three types of angles that exist in triangles
- Explain how both the shape and the angle classifications can be used to identify triangles

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
2 in chapter 14 of the course:

Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

- Go to Logic

- Go to Sets

- Properties of Shapes: Rectangles, Squares and Rhombuses 5:46
- Properties of Shapes: Triangles 5:09
- Area of Triangles and Rectangles 5:43
- Circles: Area and Circumference 8:21
- The Pythagorean Theorem: Practice and Application 7:33
- How to Identify Similar Triangles 7:23
- Applications of Similar Triangles 6:23
- Parallel, Perpendicular and Transverse Lines 6:06
- Types of Angles: Vertical, Corresponding, Alternate Interior & Others 10:28
- Angles and Triangles: Practice Problems 7:43
- Properties of Shapes: Circles 4:45
- Go to Geometry

- Inclusion in Recruitment, Interviews & Hiring
- Computer Science 105: Introduction to Operating Systems
- High School 101: High School Readiness
- Communications 301: Diversity and Intercultural Communication
- Communications 106: Communication in the Digital Age
- Operating System Fundamentals
- Cultural Differences in Nonverbal Communication
- Techniques for Inclusive Hiring & Onboarding
- Intro to Inclusion in Recruitment, Interviews & Hiring
- Implementing Inclusion in Recruitment & Screening
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines
- CLEP Exam List & Credits Offered

- What is ADA Compliance? - Definition & Guidelines
- How Are Volcanoes Formed? Lesson for Kids
- Ethical Theories in Business: Applications & Differences
- The Working Capital Ratio: Formula & Use
- How to Draft a Job Ad that Promotes Inclusion
- Bell v. Wolfish Supreme Court Case: Decision & Dissenting Opinion
- Nonlinear Functions Lesson Plan
- Non-Accidental Brain Trauma: Signs, Treatment & Ethical Considerations
- Quiz & Worksheet - Personification in The Most Dangerous Game
- Quiz & Worksheet - Food Chain of a Deciduous Forest
- Quiz & Worksheet - Characteristics of TURP Surgery
- Quiz & Worksheet - Virtue Ethics vs. Deontology
- Quiz & Worksheet - Domestic Tourism & Travel Organizations
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- Major Eras in World History Study Guide
- NES Earth & Space Science - WEST (307): Practice & Study Guide
- Computing for Teachers: Professional Development
- FTCE Biology Grades 6-12: Practice and Study Guide
- TExES Physics/Mathematics 7-12 (243): Practice & Study Guide
- TExMaT Master Mathematics Teacher 8-12: Algebraic Expressions
- WEST Business & Marketing Education: Strategic Decision Making
- Quiz & Worksheet - Self Government
- Quiz & Worksheet - Folkways in Sociology
- Quiz & Worksheet - Physical Settings & Early Civilizations
- Quiz & Worksheet - Origins & Characteristics of Polytheism
- Quiz & Worksheet - Math with Positive Integers

- The African Union's History & Purpose
- How to Register an Athlete With the NCAA Eligibility Center
- The New SAT Score Conversion
- Common Core State Standards in Missouri
- AP Spanish Exam Format
- Analytical Reasoning Questions on the LSAT
- Common Core State Standards in Idaho
- Excelsior College BS in Business Degree Plan Using Study.com
- How to Study for SAT Subject Tests
- Best GMAT Prep Book
- What Classes Can You CLEP Out Of?
- How to Use Study.com in the Classroom

Browse by subject