Triangle ticks. An equilateral triangle has the same pattern on all 3 sides, an isosceles triangle has the same pattern on just 2 sides, and a scalene triangle has different patterns on all sides since no sides are equal. Similarly, patterns of 1, 2, or 3 concentric arcs inside the angles are used to indicate equal angles. An equilateral triangle has the same pattern on all 3 angles, an isosceles triangle has the same pattern on just 2 angles, and a scalene triangle has different patterns on all angles since no angles are equal. Triangles can also be classified according to
Incircle and excircles of a triangle Because the Incenter is the same distance of all sides the trilinear coordinates for the incenter are The barycentric coordinates for a point in a triangle give weights such that the point is the weighted average of the triangle vertex positions. Barycentric coordinates for the incenter are given by where formula_7, formula_8, and formula_9 are the lengths of the sides of the triangle, or equivalently (using the law of sines) by where formula_11, formula_12, and formula_13 are the angles at the three vertices. The Cartesian coordinates of the incenter are a weighted average of the coordinates of the three vertices