# SSSTriangle

SSSTriangle[a,b,c]

returns a filled triangle with sides of lengths a, b, and c.

# Details • SSSTriangle is also known as side-side-side triangle.
• SSSTriangle can be used as a primitive in 2D graphics and as a geometric region in 2D.
• The given (blue) and computed (red) parameters for an SSSTriangle:
• • SSSTriangle returns a Triangle with A at the origin, B on the positive axis, and C in the half-plane .
• SSSTriangle allows the lengths a, b, and c to be any positive numbers such that each of them is less than the sum of the other two.

# Background & Context

• SSSTriangle constructs a side-side-side triangle. In particular, SSSTriangle[a,b,c] returns the Triangle in with vertices , and located at the origin, on the positive axis and in the upper half-plane, respectively, with a, b and c the lengths of the sides opposite vertices , and . By the SSS theorem, the triangle so specified is unique (up to geometric congruence). The arguments of SSSTriangle may be any positive numbers (exact or approximate) such that each is less than the sum of the other two (i.e. such that the triangle inequality is satisfied).
• The Triangle objects returned by SSSTriangle can be used as 2D graphics primitives or geometric regions.
• SSSTriangle is related to a number of other symbols. AASTriangle, ASATriangle and SASTriangle return two-dimensional triangles constructed using different angle and/or side specifications. Finally, SSSTriangle is a special case of Triangle, in the sense that SSSTriangle[a,b,c] is equivalent to Triangle[{{0,0},{c,0},{y,z}}] for y(-a^2+b^2+c^2)/(2 c) and z==Sqrt[(a+b-c)(a-b+c) (-a+b+c) (a+b+c)]/(2 c).

# Examples

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## Basic Examples(4)

A triangle with , , and :

 In:= Out= An SSSTriangle:

 In:= Out= Different styles applied to SSSTriangle:

 In:= Out= Area and centroid:

 In:= In:= Out= Centroid:

 In:= Out= ## Neat Examples(1)

Introduced in 2014
(10.0)