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Geometry: High School15 chapters | 160 lessons

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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.

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.

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.

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.

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.

On a stage, we say things like down stage left or up stage center. In a triangle, we use terms like adjacent and opposite. These refer to sides in relation to angles. In our musical triangle, the drummer is at one angle in the back. This side, where the audience is, is called the opposite side. That's what you'd expect, right? The opposite side is opposite the angle in question.

The adjacent sides are the sides next to the drummer. They're adjacent to the angle. For the guitarist in this angle, the side over here is the opposite side and these two sides are adjacent. These are relative terms that change based on the angle we're discussing.

We learned that a triangle is a two-dimensional shape with three sides and three angles. Each corner is called a vertex, or vertices for more than one. We can label one side as the base. Then, a perpendicular line from the base to the top, or apex, of the triangle is its height. Each angle has an opposite side, the side furthest from the angle. The sides next to the angle are called adjacent sides.

As a result of studying this lesson, you could be prepared to:

- Note the characteristics of a triangle
- Identify the three sides and three angles
- Recognize the base and height
- Locate the opposite and adjacent sides

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Geometry: High School15 chapters | 160 lessons

- Area of Triangles and Rectangles 5:43
- Perimeter of Triangles and Rectangles 8:54
- How to Identify Similar Triangles 7:23
- Angles and Triangles: Practice Problems 7:43
- Triangles: Definition and Properties 4:30
- Interior and Exterior Angles of Triangles: Definition & Examples 5:25
- Constructing the Median of a Triangle 4:47
- Median, Altitude, and Angle Bisectors of a Triangle 4:50
- Constructing Triangles: Types of Geometric Construction 5:59
- Properties of Concurrent Lines in a Triangle 6:17
- Go to High School Geometry: Properties of Triangles

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