Which of the following shapes cannot have symmetry?

The correct answer is based on the concept of symmetry, which refers to a shape being identical on both sides of a line or around a point. A shape is symmetrical if there exists at least one line (line symmetry) or point (rotational symmetry) that divides the shape into two equal parts that are mirror images.

A scalene triangle, which is defined as a triangle with all sides of different lengths, does not have any lines of symmetry because there is no way to draw a line through the shape that would create two equal halves. Each side is unique in length and angle, resulting in a configuration that does not allow for reflection or mirroring.

In contrast, a circle has infinite lines of symmetry since any diameter you draw through the center divides it into two equal halves. An oval can also have symmetry; for example, it may possess two axes of symmetry depending on its proportions. An equilateral triangle, with all sides equal, has multiple lines of symmetry, specifically three, as you can draw symmetrical lines through each vertex to the midpoint of the opposite side.

Hence, the inconsistencies in symmetry, specifically the absence of any correspondences between sides and angles, underscore why the scalene triangle does not exhibit symmetry.