**Some shapes that have no lines of symmetry include the scalene triangle and trapezium.** A trapezium is a four-sided flat shape with straight sides, none of which are parallel. Outside of the United States, the trapezium is called the general irregular quadrilateral.

A line of symmetry is a line that divides a figure into two corresponding parts, each of which is the mirror image of the other. The line of symmetry is also called the mirror line and can occur in any direction. Line symmetry is also known as reflection symmetry, mirror symmetry, mirror-image symmetry or bilateral symmetry. A line of symmetry occurs in two-dimensional objects, while a plane of symmetry occurs in three-dimensional ones.

A triangle is a polygon with three edges and three vertices. Its angles always add up to 180 degrees. There are three main types of triangles that are classified according to the relative lengths of their sides: equilateral, isosceles and scalene. In an equilateral triangle, all sides have the same length. In an isosceles triangle, two sides are equal in length. In a scalene triangle, all sides are unequal and all angles are unequal. A right triangle that is not isosceles is also a scalene triangle.