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A triangle is a polygon with three angles and three sides.

Triangles can be classified either according to their side lengths or to their internal angle measures.

The following table lists all the different types of triangles according to their corresponding classification.

Classification of Triangles | |
---|---|

By Side | By Angle |

Scalene triangle | Acute triangle |

Isosceles triangle | Right triangle |

Equilateral triangle | Obtuse triangle |

A scalene triangle is a triangle in which all three sides have different lengths.

An isosceles triangle is a triangle that has two congruent sides called *legs*. The angle between these two sides is called vertex angle and its opposite side is called *base*. The angles formed by the legs and the base are called *base angles*. Base angles are congruent.

An obtuse triangle is a triangle that contains exactly one obtuse angle. Therefore, an obtuse triangle has an angle whose measure is greater than $90_{∘}$ or $2π $ radians.

A right triangle is a specific type of triangle that contains a right angle. The side that lies opposite the right angle is always the longest and is known as the hypotenuse. The other sides are commonly called legs.

If one of the acute angles in the triangle is labeled, the legs can be discussed relative to that angle. Consider an acute angle labeled as $∠θ$ on the diagram. The side that forms the angle is the adjacent side and the side not touching the angle is the opposite side. Note that the opposite and adjacent sides change when $∠θ$ changes, but the hypotenuse is always the same.

An equiangular triangle is a triangle with three congruent angles, all measuring $60_{∘}$ or $3π $ radians.

In an equiangular triangle, all sides are congruent. Therefore, they are also known as equilateral triangles. {{ 'ml-article-textbook-solutions-description' | message }}

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