Triangle

Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

Types of triangles

Triangles can be classified according to the lengths of their sides:

• An equilateral triangle has all sides the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.
• An isosceles triangle has two sides of equal length. An isosceles triangle also has two angles of the same measure.
• A scalene triangle has all sides and all angles of different lengths and measures, respectively.

Triangles can also be classified according to their internal angles:

• A right triangle has one of its interior angles measuring 90°. The side opposite to the right angle is the hypotenuse.
• An obtuse triangle has one of its interior angles measuring more than 90°.
• An acute triangle has all of its interior angles measuring less than 90°.

Properties

Triangles have several properties, including:

• The sum of the measures of the angles of a triangle is 180 degrees.
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem.
• The sum of the lengths of any two sides of a triangle always exceeds the length of the third side, a principle known as the triangle inequality.

See also

• Pythagorean theorem
• Heron's formula
• Triangle inequality
• Trigonometry

Triangle Resources
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