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Triangles can be classified into three types: Equilateral, isosceles, and scalene.

An Equilateral triangle is just what it sounds like: a triangle with all its sides equal.

Because all of its sides are equal, it follows that all of its angles are also equal.

A second type of triangle is the isosceles triangle. This type of triangle has at least two sides equal; thus, an equilateral triangle is also an isosceles.

An isosceles triangle also has the property that the two angles opposite the two equal sides are also equal.

The last type of triangle is the scalene triangle. This triangle has no three sides equal; in other words, all the sides are of different lengths.

As you can guess, all the angles of this triangle also are distinct.

All triangles can be categorized into two mutually exclusive classes of triangles: isosceles and scalene. An isosceles triangles has at least two sides which are equal in length, and a scalene triangle has no two sides which are equal. You may notices that because of this, isosceles triangles always have at least one line of symmetry while scalene triangles do not have any. An equilateral triangle is a special case of an isosceles triangle that has all three sides equal in length. As a result, all equilateral triangles have three lines of symmetry and three angles equal to $60^\circ$.

Here is some extra practice on identifying different types of triangles based on their sides. Be warned, this worksheet uses variables instead of numbers; just assume each variable is distinct. GLHF!

Triangles are usually divided into three types based on the the lengths of their sides:

$1) Equilateral$

$2) Isosceles$

$3) Scalene$

An $equilateral$ triangle is the one having all the three sides equal in length.

It follows that all of its angles are equal in measure.

An $isosceles$ triangle is one having two of its sides equal in length.

It follows that the two angles opposite to the two equal sides are equal in measure.

An $scalene$ triangle is the one having all the sides different in length.

It follows that all of its angles are unequal in measure.