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Triangles: Definition and Properties

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  • 0:07 What is a Triangle?
  • 0:57 Sides and Angles
  • 1:30 Base and Height
  • 3:04 Opposite and Adjacent
  • 3:57 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

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

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.

What Is a Triangle?

You're probably familiar with the prefix 'tri-.' It pops up in a lot of places. There's trilogy - like the Star Wars trilogy (okay - trilogies). There's triathlon, with its running, cycling and swimming. There's trio, like Nirvana or Destiny's Child.

What do all these have in common? Hmm, was Beyonce in Star Wars? No. All these tri- things have three of something. A movie trilogy has three movies. A triathlon has three events. And a trio has three members.

And this is where a triangle gets its name and defining characteristics. A triangle is a two-dimensional shape with three sides and three angles. Triangle - three angles. Yep, it's as simple as that.

Sides and Angles

A power trio needs a guitar, drums and bass. Likewise, a triangle has a few parts that come in threes. There are its three sides. Then there are the three angles. Without these sides and angles, it's not a triangle.

You might hear these corners referred to as vertices (or vertex if it's just one). Vertex isn't unique to triangles; it refers to the corner of any shape. And in the triangle, there are three vertices.

Base and Height

When you have a musical trio, like the Police, you usually have three people who all want to be the star. But while Stewart Copeland and Andy Summers can be awesome, they're not Sting. Sting is the star. I mean, he doesn't even have a normal name. His name is what bees do.

It's no different in a triangle. Sure, they all have three sides. But when we work with triangles, we need a point of reference. There has to be a spokesperson.

That's where the base comes in. The base is one side of the triangle. It's usually the bottom, but you can call any side the base; it doesn't matter. (Don't tell Sting we said that.) The base is useful when we want to identify the dimensions of a triangle, such as when we're finding its area.

The other dimension we want is the height. Wait, the what? Is it just another side? No. Think of the triangle like a mountain. I live near the Rockies, so I'm often looking at 14,000-foot peaks and thinking about their amazing height.

If a mountain is 14,000 feet, that's not the length of the trail to its top. No, it's the perpendicular distance from the base to the top (well, supposing the base is sea level). For a triangle, the height is the same - the perpendicular distance from the base to the top. As with a mountain, this is sometimes also called the altitude. Oh, and the top can also be called an apex. This is also like a mountain. Apex is just another word for the highest point, or summit.

Opposite and Adjacent

You know how a three-person band is usually set up? The drummer is in the middle, in the back. Towards the front, to one side, is the guitarist. On the other side is the bass player.

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