Classifying triangles

Classifying triangles

Lessons

In this lesson, we will learn:

  • How to classify triangles by their side lengths
  • How to classify triangles by their angles

Notes:

  • A triangle is a 2-dimensional (2D) shape with 3 straight sides and 3 angles
    • A triangle’s angles always add up to 180° degrees

  • Triangles can be classified in 2 ways:
    1. By their side lengths
    2. By the size of their angles

  • When looking at side lengths, we classify triangles by how many sides are the same length (how many sides are “congruent”)
    • If no sides are the same, it is a scalene triangle
    • If two sides are the same, it is an isosceles triangle
    • If all three sides are the same, it is an equilateral triangle

  • When looking at the angles, we classify triangles by its biggest angle and comparing it with the right angle (are the angles smaller than, equal to, or greater than 90° degrees?)
    • If all of the angles are smaller than 90° , it is an acute triangle
    • If one of the angles is exactly 90° , it is a right triangle
    • If one of the angles is bigger than 90° , it is an obtuse triangle

Angles and Polygons: Classifying triangles
  • Introduction
    Introduction to Classifying triangles:
    a)
    What are the basic characteristics of triangle shapes/polygons?

    b)
    How to classify triangles by their side length

    c)
    How to classify triangles by their angles

    d)
    Review on the six classifications for triangles


  • 1.
    Classifying triangles by side lengths
    Classify the triangle by its side lengths. Is it scalene, isosceles, or equilateral?
    a)

    Angles and Polygons: Classifying triangles

    b)

    Angles and Polygons: Classifying triangles

    c)

    Angles and Polygons: Classifying triangles

    d)

    Angles and Polygons: Classifying triangles

    e)

    Angles and Polygons: Classifying triangles

    f)

    Angles and Polygons: Classifying triangles


  • 2.
    Classifying triangles by angles
    Classify the triangle by its angles. Is it acute, right, or obtuse?
    a)

    Angles and Polygons: Classifying triangles

    b)

    Angles and Polygons: Classifying triangles

    c)

    Angles and Polygons: Classifying triangles

    d)

    Angles and Polygons: Classifying triangles

    e)

    Angles and Polygons: Classifying triangles

    f)

    Angles and Polygons: Classifying triangles


  • 3.
    Classifying triangles by more than one type
    Classify the triangle by BOTH its side length and angles. (scalene, isosceles, or equilateral; acute, right or obtuse)
    a)

    Angles and Polygons: Classifying triangles

    b)

    Angles and Polygons: Classifying triangles

    c)

    Angles and Polygons: Classifying triangles


  • 4.
    Word Problems: Classifying Triangles
    Use this figure to answer the following questions:
    Angles and Polygons: Classifying triangles
    a)
    If a triangle's side lengths are: 2cm, 1cm, and 1.73cm how would you classify it and why?

    b)
    If this triangle is a right triangle, what types of angles does it have?

    c)
    Is it possible for this triangle to have an obtuse angle? Why or why not?

    d)
    If this right triangle has one angle that is 30°, give the measures of all three of the angles.