The points A, B, and C are collinear if AB + BC = AC.
Three points A, B, and C are the vertices of an equilateral triangle if AB = BC = CA.
Points A, B, and C are the vertices of an isosceles triangle if AB = BC or BC = CA, or CA = AB.
Three points A, B, and C are the vertices of a right triangle if the sum of squares of any two sides is equal to the square of the third side.