Types of triangles

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

• Equilateral Triangle: All three sides are equal. Therefore, its three angles are also equal. That is to say:
  

  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°.



• Isosceles Triangle: It has two equal sides. Hence, it also has two equal angles.
  

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



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

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°).

Summary: Types of Triangles

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