How do you identify the lines of symmetry in a cone?

A cone has an infinite number of lines of symmetry that all pass through its apex and centre of the base.

To understand this better, imagine a cone standing upright on its circular base. The apex is the pointed top of the cone, and the base is the flat circular bottom. Any line that you draw from the apex, through the centre of the base, and extending to the opposite side of the base, will be a line of symmetry. This is because if you were to fold the cone along this line, both halves would match perfectly.

The reason there are infinite lines of symmetry is due to the circular base. You can draw these lines at any angle around the circle, and each one will still divide the cone into two identical halves. This is different from shapes like squares or rectangles, which have a limited number of lines of symmetry.

Visualising this can be easier if you think of slicing the cone with a plane that passes through the apex and the centre of the base. Each slice will create two mirror-image halves, demonstrating the line of symmetry. This property is unique to cones and other shapes with rotational symmetry around a central axis.