What Is an Isosceles Triangle?

Known as the “Father of Geometry,” mathematician Euclid lived around 300 BC. He came up with the rules involving isosceles triangles. But, what is an isosceles triangle? How is it different from other triangles? And how can you calculate its height, perimeter, and area? Here are the answers to these questions and more. And be sure to enjoy other videos in our Geometry series!

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What Is an Isosceles Triangle?

Isosceles comes from the Greek words “isos” (meaning equal) and “skelos” (meaning leg). As this name suggests, an isosceles triangle has two equal sides with two equal angles opposite of those sides. Some of the other types of triangles include:

  • Right triangle- a triangle with one right angle (equaling 90 degrees)
  • Equilateral triangle- a triangle with three equal sides and angles
    • Every equilateral triangle could also be considered an isosceles triangle, but not every isosceles triangle is equilateral.
  • Scalene triangle- a triangle with no equal sides
  • Acute triangle- a triangle where all three angles are acute (less than 90 degrees)
  • Obtuse triangle- a triangle with one angle that is obtuse (more than 90 degrees)
  •  
    Therefore, depending on the side and angle measurements, your isosceles triangle could be an acute, obtuse, right, or equilateral triangle as well.

    Parts of an Isosceles Triangle

    The two equal sides of the isosceles triangle are legs and the third side is the base. The angle between the equal sides is called the vertex angle. All of the angles should equal 180 degrees when added together.

    Height

    If you were to draw an imaginary line from the vertex angle to the base (at a 90-degree angle from the base), you would get the height of your isosceles triangle. To calculate the height, you should use the following equation:
    what is an isosceles triangle - magoosh

    The “a” is the leg length, and the “b” is the base length. After inputting these numbers into the equation, you can simplify it using the order of operations to determine the length of the height.

    Perimeter

    The perimeter is the measurement around the outside of the shape. To calculate this, you just need to add the length of each side. However, since there are two sides with the same length, you can simplify it to the following equation:
    p = 2a + b

    Area

    Area is the amount of unit squares that can fit within the given shape. To determine the area of an isosceles triangle, you can use the following formula:
    what is an isosceles triangle, area - magoosh

    As shown in the equation, you’ll need the measurement for the base and height. If the height measurement isn’t given, you can use the height equation first. Then, input the numbers and solve for the area.

    To calculate the height, perimeter, and area of a triangle, you need to be able to identify the type of triangle first. That way you can use the proper equations to get accurate results.

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    Author

    • Jamie Goodwin

      Jamie graduated from Brigham Young University- Idaho with a degree in English Education. She spent several years teaching and tutoring students at the elementary, high school, and college level. She currently works as a contract writer and curriculum developer for online education courses. In her free time, she enjoys running and spending time with her boys!

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