Symmetry - Figures with one, two or multiple Lines of Symmetry

Line Symmetry: A figure has line symmetry if a line can be drawn through it such that the figure can be folded along that line into two identical parts that coincide exactly. This is also called mirror symmetry because one half of the figure is the mirror reflection of the other.

Line of Symmetry: The imaginary line that divides a symmetrical figure into two identical halves is called the line of symmetry or axis of symmetry. For instance, in the letter $M$, a vertical line drawn through the center peak creates two matching halves.

Figures with One Line of Symmetry: Some figures possess only a single axis of symmetry. An isosceles triangle has exactly one line of symmetry which passes through the vertex between the two equal sides and is perpendicular to the base. Other examples include the letters $A, T, U,$ and $V$.

Figures with Two Lines of Symmetry: A rectangle is a figure with two lines of symmetry: one vertical line and one horizontal line, both passing through the center and connecting the midpoints of opposite sides. Note that the diagonals of a rectangle are NOT lines of symmetry as the halves do not match when folded.

Symmetry in Regular Polygons: A regular polygon (where all sides and angles are equal) has multiple lines of symmetry. The number of lines of symmetry is equal to the number of its sides. For example, an equilateral triangle has $3$ lines, a square has $4$ lines, a regular pentagon has $5$ lines, and a regular hexagon has $6$ lines.

Infinite Lines of Symmetry: A circle is the most symmetrical figure because it has an infinite number of lines of symmetry. Every straight line (diameter) that passes through the center of the circle divides it into two identical semicircles.

Reflection and Symmetry: Symmetry is deeply connected to reflection. When a figure is symmetrical, the line of symmetry acts as a mirror line. The distance of any point on the original shape to the line of symmetry is exactly equal to the distance of the corresponding point in the reflected half to that same line.