Search results
Results From The WOW.Com Content Network
Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given ...
If one of three given lengths is equal to the sum of the other two, the three sides determine a degenerate triangle, a line segment with zero area. In this case, the semiperimeter will equal the longest side, causing Heron's formula to equal zero.
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [1] [2] Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84.
The (3, 5, 7) triangle and its multiples are the only triangles with a 120° angle and having integer sides in arithmetic progression. [39] The only integer triangle with area = semiperimeter [40] has sides (3, 4, 5). The only integer triangles with area = perimeter have sides [40] [41] (5, 12, 13), (6, 8, 10), (6, 25, 29), (7, 15, 20), and (9 ...
Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle. [15] The incircle radius is no greater than one-ninth the sum of the altitudes. [16]: 289
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
A general form triangle has six main characteristics (see picture): three linear (side lengths a, b, c) and three angular (α, β, γ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any of the following: [1] [2]
[16] [17] Other triangle centers also associated with the Malfatti circles include the Yff–Malfatti point, formed in the same way as the first Malfatti point from three mutually tangent circles that are all tangent to the lines through the sides of the given triangle, but that lie partially outside the triangle, [18] and the radical center of ...