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    Home
    Algebra
    Math Games
  • Decimals in Space
  • Fraction Balls
  • Integers in Space
  • Math Man
  • Number Balls
  • Geometry
    Interactive
    Trigonometry
    Jobs
  • Tutoring jobs
  • New York Tutoring Jobs
  • White Plains, NY
  • Westchester County, NY
  • Chicago Math Jobs
  • Philadelphia
  • Teacher Resources
    On FaceBook!

    Triangles Side and Angles

    Interior & Exterior Angles and sides

    Properties of Triangles



    Triangles are one of the most fundamental geometric shapes and have a variety of often studied properties relating to their
    What is the difference between interior and exterior angles of a triangle?
    This question is answered by the picture below. You create an exterior angle by extending any side of the triangle. Web page on the relationship between exterior and interior angles of a triangle
    Picture of interior and exterior angles of a triangle

    Interior Angles of a Triangle Rule



    This may be one the most well known mathematical rule--The sum of all 3 interior angles in a triangle is 180°. As you can see from the picture below, if you add up all of the angles in a triangle the sum must equal 180°. This property of a triangle's interior angles is simply a specific example of the general rule for any polygon's interior angles.

    Interior Angle Sum of triangle is 180
    To explore the truth of this rule, try Math Warehouse's interactive triangle, which allows you to drag around the different sides of a triangle and explore the relationship between the angles and sides. No matter how you position the three sides of the triangle, the total degrees of all interior angles (the three angles inside the triangle) is always 180°.


    Interactive Demonstration of Interior Angle Sum

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    Practice Problems on Interior Angles of a Triangle Rule



    What is mLNM in the triangle below?
    Answer

    LMN = 34°
    MLN = 29°
    A triangle's interior angles are HOP, HPO and PHO.
    HOP is 64° and mHPO is 26°.
    What is mPHO?
    Answer



    Relationship between Side Lengths and Angle Measurements



    Worksheet on the relationship between the side lengths and angle measurements of a triangle
      In any triangle,
    • the largest interior angle is opposite the largest side.
    • the smallest interior angle is opposite the smallest side
    • the middle-sized interior angle is opposite the middle-sized side
    Largest angle vs largest side To explore the truth of the statements you can use Math Warehouse's interactive triangle, which allows you to drag around the different sides of a triangle and explore the relationships betwen the measures of angles and sides. No matter how you position the three sides of the triangle, you will find that the statements in the paragraph above hold true.(All right, the isosceles and equilateral triangle are exceptions due to the fact that they don't have a single smallest side or, in the case of the equilateral triangle, even a largest side. Nonetheless, the principle stated above still holds true. !)
    Interactive Demonstration of Side Length vs Angle Measure

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