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SASTriangle—Wolfram Language Documentation

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• See Also
  • Triangle
  • SSSTriangle
  • ASATriangle
  • AASTriangle
  • Polygon
• Related Guides
  • Graphics Objects
  • Basic Geometric Regions
  • Plane Geometry
  • Solid Geometry
  • Polygons

SASTriangle[a,γ,b]

returns a filled triangle with sides of length a and b and angle γ between them.

• SASTriangle constructs a side-angle-side triangle. In particular, SASTriangle[a,γ,b] represents the Triangle in with vertices , and located at the origin, on the positive axis and in the upper half-plane, respectively, with a and b the lengths of the sides opposite vertices and and γ. By the SAS theorem, the triangle so specified is unique (up to geometric congruence). SASTriangle allows the lengths a and b to be any positive numbers and the angle γ to be a positive value satisfying . The arguments of SASTriangle may be exact or approximate numeric expressions.
• The Triangle objects returned by SASTriangle can be used as 2D graphics primitives or geometric regions.
• SASTriangle is related to a number of other symbols. AASTriangle, ASATriangle and SSSTriangle return two-dimensional triangles constructed using different angle and/or side specifications. SASTriangle is a special case of Triangle, in the sense that SASTriangle[a,γ,b] is equivalent to Triangle[{{0,0},{x,0},{y,z}}] for xSqrt[a^2+b^2-2 a b Cos[γ]], y(b^2-a bCos[γ])/Sqrt[a^2+b^2-2 a b Cos[γ]] and z(a b Sin[γ])/Sqrt[a^2+b^2-2 a b Cos[γ]].

SASTriangle evaluates to Triangle with one point at the origin and one edge on the axis:

A triangle with symbolic edge length:

Plot them:

Color directives specify the face color:

FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

Embedding dimension is the dimension of the space the triangle lives in:

Geometric dimension is the dimension of the shape itself:

Membership testing:

Conditions for membership:

Area:

Centroid:

Distance from a point to an SASTriangle:

Visualize it:

Signed distance from a point:

Now plot it:

Nearest point:

Visualize it:

A triangle is bounded:

Find its range:

Integrate over an SASTriangle:

Optimize over it:

Solve equations over an SASTriangle:

A triangle with two equal sides is an isosceles triangle:

Visualize it:

Find its area:

The circumcircle of an SASTriangle can be found using Circumsphere:

The circumcircle passes through the three corner points:

Find the midpoints for each edge of the triangle:

The perpendicular bisectors are lines from the circumcenter to the midpoints:

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