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In this lesson, you’ll learn how to find the altitude of a triangle, including equilateral, isosceles, right and scalene triangles. You’ll also find out why all triangles have three altitudes.

Altitude in Triangles

Did you ever stop to think that you have something in common with a triangle? Well, you do! Both people and triangles can be measured according to their height. For example, when you have your school physical, the doctor will measure how tall you are in feet and inches.But if you were a triangle, we’d describe your height, or tallness, as altitude. You may have heard the word altitude before, especially if you live in or around any mountains. The height of a mountain is measured in feet and referred to as its altitude.

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Now, let’s go ahead and measure the altitude of four different types of triangles: equilateral, isosceles, right, and scalene triangles.

Altitude in Equilateral Triangles

First, let’s take a look at the altitude, or height, of an equilateral triangle, which has three equal sides. The way to measure the altitude of this triangle is to pick a corner, or vertex, of the triangle. Then, draw a line straight to the bottom, or the base, of the triangle at a right angle. The length of the line you have drawn is the altitude. If you draw a line from any of the three sides of an equilateral triangle, it will always be the same length. Therefore, all three altitudes will be the same.

Isosceles ; Right Triangles

An isosceles triangle, has two equal sides. It also has three altitudes; however, just two of them are the same length.A right triangle has one right angle and three altitudes, or lengths. Two of the sides meet at a 90-degree angle, where they form the legs of the triangle.

Scalene Triangles

Scalene Triangle
scalenetriangle

Some triangles look like they have a ledge. These kinds of triangle are more difficult to measure, because when you draw a line from the vertex to the base to make a right angle, you’ll find that the base will be on the outside of the triangle. A triangle that has three different sides or lengths is called a scalene triangle. However, not all scalene triangles look alike, and not all of them have ledges.

Scalene Triangles
scalenetriangles

Lesson Summary

The altitude, also known as the height, of a triangle is determined by drawing a line from the vertex, or corner, of the triangle to the base, or bottom, of the triangle. All triangles have three altitudes.

  • An equilateral triangle has three equal sides and altitudes
  • An isosceles triangle has two equal sides and altitudes
  • A right triangle has two sides that meet at a 90-degree angle
  • A scalene triangle, which has three unequal sides, can present some challenges while measuring because when we draw a line from the vertex to the base to make a right angle, the base falls on the outside of the triangle

Learning Outcomes

When you’ve watched and reviewed this lesson, see if you have retained enough information to:

  • Identify the different types of triangles
  • Find the altitude of isosceles, right, scalene and equilateral triangles

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