- has an infinite number of lines of symmetry
A circle has an infinite number of lines of symmetry.
An object can have an infinite number of lines of symmetry if it is infinitely long and symmetric. For example, an infinite line or a line segment that extends indefinitely in both directions has an infinite number of lines of symmetry. Any line passing through the midpoint of the line segment will divide it into two equal halves, making it symmetrical. Since there are an infinite number of possible lines passing through the midpoint, the line segment has an infinite number of lines of symmetry.
To determine if a shape has an infinite number of lines of symmetry, we need to understand the concept of symmetry.
Symmetry refers to a balanced and identical reflection of an object or shape when it is divided into two equal parts. A line of symmetry is an imaginary line that divides an object or shape into two congruent halves that are mirror images of each other.
Now, to answer your question, if a shape has an infinite number of lines of symmetry, it means that there are an unlimited number of lines that can divide the shape into two equal halves.
One example of a shape with infinite lines of symmetry is a circle. A circle has an infinite number of lines of symmetry because you can draw a line through its center in any direction, and both halves will be identical.
To verify this, you can take a circle and draw various lines passing through its center in different directions. Regardless of the angle or position of these lines, the two halves of the circle will always be symmetrical.
Hence, a circle is an example of a shape that has an infinite number of lines of symmetry.