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Theory

Triangles

Concept

Triangle

A triangle is a polygon with three angles and three sides.
Interactive triangle with movable vertices
Triangles can be classified either according to their side lengths or to their internal angle measures.
Interactive triangle with one movable vertex
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

Concept

Scalene Triangle

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

Scalene Triangle

Concept

Isosceles Triangle

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.

Isosceles triangle

Concept

Equilateral Triangle

An equilateral triangle is a triangle in which all the sides are congruent.

Equilateral triangle
Equilateral triangles are also known as equiangular triangles, since all angles are congruent and have a measure of or radians.

Concept

Acute Triangle

An acute triangle is a triangle where all angles are acute. This is, all angles measure less than or radians.

Acute triangle

Concept

Obtuse Triangle

An obtuse triangle is a triangle that contains exactly one obtuse angle. Therefore, an obtuse triangle has an angle whose measure is greater than or radians.

Obtuse triangle

Concept

Right Triangle

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.

Right triangle
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 on the diagram. The side that forms the angle is the adjacent side and the side not touching the angle is the opposite side.
Sides of a right triangle labeled
Note that the opposite and adjacent sides change when changes, but the hypotenuse is always the same.

Concept

Equiangular Triangle

An equiangular triangle is a triangle with three congruent angles, all measuring or radians.

Equiangular triangle
In an equiangular triangle, all sides are congruent. Therefore, they are also known as equilateral triangles.

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