Types of triangles

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Triangles can be classified by their sides or by their angles. According to these, we can assert that there are basically six different types of triangles: equilateral triangle, isosceles triangle, scalene triangle, right triangle, acute triangle, and obtuse triangle.

By Side

    Drawing of the equilateral triangle with its sides and interior angles

  • Equilateral Triangle: All three sides are equal. Therefore, its three angles are also equal. That is to say:
    Equilateral Triangle Side and Angle Ratio Formula

    Since all angles are equal and add up to 180° (why do angles add up to 180°?), they are all 60° α=β=γ=60°.

  • Dibujo del triángulo isósceles con sus lados y ángulos interiores

  • Isosceles Triangle: It has two equal sides. Hence, it also has two equal angles.
    Isosceles Triangle Side and Angle Ratio Formula

    As we see in the image above, the unequal angle β is the one formed by the two equal sides (a and c).

  • Dibujo del triángulo escaleno con sus lados y ángulos interiores

  • Scalene Triangle: All three sides are unequal, so their three angles are different too from each other. Therefore, we have that:
    Scalene Triangle Side and Angle Ratio Formula

By Angle

  • Right Triangle: It has one angle equal to 90 degrees. The other two are acute angles, i.e. they measure less than 90 degrees.
  • Oblique Triangle: It hasn’t any angle measuring 90 degrees. Oblique triangles can be classificated in:
    • Acute Triangle: all three angles are acute, that is, its angles measure less than 90°.
    • Obtuse Triangle: One of its angles is greater than 90°. The other two are acute (less than 90°).
Drawing of triangle types according to their angles

Summary: Types of Triangles

The table below shows the different types of triangles based on sides and angles:

Tabla de los tipos de triángulo según sus ángulos y lados

AUTHOR: Bernat Requena Serra

YEAR: 2020


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