triangle
Sign in to savethumb|Triangle, a polygon with three corners (vertices) and three lines (sides) A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is
AI overview
A triangle is a basic geometric shape made up of three corners (called vertices) and three straight sides (called edges) that connect them. Triangles are important in geometry and mathematics because their internal angles always add up to 180 degrees, which is a fundamental property that makes them useful for understanding shapes and solving practical problems.
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Article
24 sectionsContents
- Definition, terminology, and types
- Appearances
- Properties
- Points, lines, and circles associated with a triangle
- Angles
- Similarity and congruence
- Area
- Possible side lengths <span class="anchor" id="Inequality"></span>
- Rigidity
- Triangulation
- Location of a point
- Related figures
- Figures inscribed in a triangle
- Figures circumscribed about a triangle
- Miscellaneous triangles
- Circular triangles
- Triangle in non-planar space
- Fractal geometry
- See also
- References
- Notes
- Footnotes
- Works cited
- External links
thumb|Triangle, a polygon with three corners (vertices) and three lines (sides) A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the height. The area of a triangle equals one-half the product of height and base length.
In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated within a unique flat plane. More generally, four points in three-dimensional Euclidean space determine a solid figure called tetrahedron.