## Classification of triangles

Triangles can be classified according to a different criteria:

- According to its sides
- According to its angles

### Classification of triangles depending on the sides

#### Equilateral triangle

If its three sides have the same length (three internal angles measuring $$60$$ degrees).

#### Isosceles triangle

If it has two sides of the same length. The angles that are opposed to these sides have the same measurement.

#### Scalene triangle

If all its sides have different lengths. In a scalene triangle there are no angles with the same measurement.

### Classification of triangles depending on the angles

#### Triangle Rectangle:

If it has a right interior angle $$(90^\circ)$$. Both sides conforming to the right angle are named leg and hypotenuse.

#### Obtuse triangle

If one of its angles is obtuse (higher than $$90^\circ$$); the other two are acute (less than $$90^\circ$$).

#### Acute angled triangle

When its three angles are less than $$90^\circ$$; the equilateral triangle is a particular case of acute angled triangle.

#### Equiangular triangle

Normally it is called an equilateral triangle and it has already been commented on previously.

## Properties of the triangles

Triangles | Equilateral | Isosceles | Scalen |
---|---|---|---|

Acute angled |
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Rectangle |
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Obstuse angled |

We can see in the previous scheme that the classifications commented on in the previous paragraph can be combined in pairs (one from every paragraph).

Thus, we have the following characteristics:

**Isosceles acute angled triangle**: All the angles are acute, two of them being equal, and the other different from these two. This triangle is symmetrical regarding the height, making it different from the others.**Acute angled scalene triangle**: All its angles are acute and all are different, it does not have symmetry axes.

The rectangular triangles can be:

**Rectangular isosceles Triangle**: with one right angle and two equal acute ones (of $$45^\circ$$ each one); two sides are equal and the other is different, naturally the equal sides are the legs, and the different one is the hypotenuse; it is symmetrical regarding the height that connects the right angle up to the hypotenuse.**Rectangular scalene triangle**: it has a right angle and all its sides and angles are different.

The obtuse triangles are:

**Isosceles obtuse triangle**: it has an obtuse angle, and two equal sides that are those that begin in the obtuse angle, the other side is bigger than the other two.**Obtuse scalene triangle**: it has an obtuse angle and all its sides are different.