Triangle
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 [math]\displaystyle{ \triangle ABC }[/math].[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.
Types of triangles
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.
|
Area
The area of a triangle is equal to base times height times one half.
[math]\displaystyle{ area= \frac{base \times height}{2} }[/math]
Triangle Media
Euler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides (i.e., equilateral triangles are isosceles).
The first page of Euclid's Elements, from the world's first printed version (1482), showing the "definitions" section of Book I. The right triangle is labeled "orthogonius", and the two angles shown are "acutus" and "angulus obtusus".
The circumcenter is the center of a circle passing through the three vertices of the triangle.
Related pages
References
- ↑ "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-01.
- ↑ Weisstein, Eric W. "Triangle". mathworld.wolfram.com. Retrieved 2020-09-01.
- ↑ 3.0 3.1 "Triangles - Equilateral, Isosceles and Scalene". www.mathsisfun.com. Retrieved 2020-09-01.