Triangle

For other uses, see Triangle (disambiguation).

A triangle is a shape, or a part of two dimensional space. It has three straight sides and three vertices. The three angles of a triangle always add up to 180° (180 degrees). It is the polygon with the least possible number of sides. A triangle with vertices A, B, C is written as ${\displaystyle \triangle ABC}$.^[1][2] The study of geometry related to triangles is called trigonometry. Modern computers usually use triangles to make more complex graphic images or shapes.

A black triangle

Types of triangles

This is an isosceles right triangle, because it has a right angle and two of its sides have the same length.

Triangles can be grouped according to how many of their sides are equal:^[3]

• if all the three sides of a triangle have the same length, then it is an equilateral triangle.
• if a triangle has two sides with the same length, then it is an isosceles triangle.
• if all the three sides of a triangle have different lengths, then we have a scalene triangle.

Triangles can also be grouped by their angles:^[3]

• if a triangle has a right angle, that is, if one of the angles of that triangle measures 90° (90 degrees), then it is a right triangle. The opposite side to the right angle is the hypotenuse.
• if a triangle has an obtuse angle, that is, if one of the angles of that triangle is larger than 90°, then it is an obtuse triangle.
• if a triangle has only acute angles, that is, if all the angles of that triangle are less than 90°, then it is an acute triangle.

Equilateral triangle Isosceles triangle Scalene triangle Right Angled triangle Obtuse Angled triangle Acute Angled triangle

Area

b is base and h is height

The area of a triangle is equal to base times height times one half.

${\displaystyle area={\frac {base\times height}{2}}}$

Related pages

• Law of sines
• Pythagorean theorem
• Sierpinski triangle
• Reuleaux triangle

References

1. "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-01.
2. Weisstein, Eric W. "Triangle". mathworld.wolfram.com. Retrieved 2020-09-01.
3. "Triangles - Equilateral, Isosceles and Scalene". www.mathsisfun.com. Retrieved 2020-09-01.