Slope Triangle: Definition & Concept

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  • 0:00 Definition Of A Slope…
  • 1:45 Slope Triangles And Graphs
  • 2:20 Negative Slope
  • 2:45 Lesson Summary
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Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

In this lesson, you will learn about slope triangles, a kind of triangle that helps you easily find the slope of a line or line segment. Often, these are imaginary triangles sketched between two points.

Definition of a Slope Triangle

A slope triangle is a visual tool that helps you find the slope of a line. By 'slope,' we mean steepness.

Imagine that you are flying a plane and have ascended (vertically) 1,000 feet. When you are 1,000 feet above the ground, you have traveled forward (horizontally) 3,000 feet. With those two measurements, you can figure out how steep your ascent was. The higher the plane rises while it travels forward a certain amount, the steeper the incline.

If you look at the picture of the airplane's ascent, you'll see a triangle. This triangle is imaginary, of course. It is a visual tool, a 'slope triangle,' that helps you calculate how steep the ascent was. In other words, it helps you figure out the slope of the line connecting the plane's starting point to its current position.

An Airplane
Slope triangle

One formula for slope you may have seen looks like this:

Slope = rise/run

The rise is the vertical distance on the triangle. The run is the horizontal distance. For our airplane, we get:

Slope = 1,000 feet/3,000 feet = 1/3

In other words, the airplane rises 1 foot vertically every time it travels 3 feet along the ground.

If a plane is 2,000 feet above the ground after it has traveled 3,000 feet forward, then its ascent is steeper. For the same horizontal distance traveled, it has reached a greater height. In this case, the slope triangle is less flat. The horizontal leg of the triangle is longer.

Slope = rise/run = 2,000 ft/3,000 ft = 2/3

The slope of the first airplane's ascent, 1/3, is less than the slope of the second airplane, 2/3. The second airplane travels upward more steeply.

An Airplane Ascending More Quickly
Slope Triangle

Slope Triangles and Graphs

Sometimes you may want to find the slope of a line, a line segment, or an imaginary line segment between two points. In the picture, the red dot is at the point (1,2). The blue dot is at the point (2,4). You can draw in a slope triangle by connecting the two points and creating the horizontal and vertical legs of a triangle.

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