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In coordinate geometry, triangles may be formed by the intersection of linear systems and linear inequalities. Some mathematical relationships that can be determined given a shaded triangular region on a coordinate axes are given below:
- The coordinates of the triangle vertices
- The equations of lines creating the sides of the triangle
- The linear inequalities that define the triangle’s perimeter and shaded region bound by these linear inequalities
- The lengths of the sides of the triangle using of the vertices and the Pythagorean theorem
- The type of the triangle (such as right, scalene, isosceles)