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Line symmetry is a form of symmetry in which one half of an object reflects the other half across a line. In simple terms, when an object is divided into two equal pieces by a line, the two sides of the line appear identical. Additionally, it is referred to as mirror symmetry or reflection symmetry. For instance, butterfly wings are identical on both sides, and the human face also exhibits line symmetry.
We shall explain the notion of the line of symmetry and its meaning in this article. Additionally, we will examine the line symmetry of various geometric shapes and the number of lines of symmetry that each shape has. Additionally, we will solve many instances to help you grasp the topic.
Line of Symmetry
A line of symmetry, alternatively referred to as a mirror line, is a line that divides an object into two identical parts. We have a square here, which we may fold into two equal half. When a figure is folded in half along its symmetry axis, both parts perfectly match. The axis of symmetry is the name given to this line of symmetry. Using a given figure, observe the various patterns of symmetry that an object can have.
Classification of the line of symmetry
• Vertical Line of Symmetry: A standing straight line can be used to divide the above shape into two identical halves. In this situation, the symmetry line is vertical.
• Horizontal Line of Symmetry: When the above shape is sliced horizontally, it can be divided into two equal halves. Consequently, the symmetry line is horizontal in this circumstance. Thus, when a shape is divided horizontally, from right to left or vice versa, the horizontal line of symmetry divides it into identical halves.
• Diagonal Line of Symmetry: The above shape can be divided into two identical halves along its diagonal line of symmetry. Taking this into consideration, the symmetry line is diagonal. When split across the diagonal corners, a diagonal line of symmetry divides a form into identical halves.
Symmetry in Shapes
In geometry, we have plane shapes with line symmetry such as the square, rectangle, triangle, rhombus, and parallelogram. The following are some common examples of the line of symmetry in two-dimensional shapes:
Square Symmetry of Lines
A square has four lines of symmetry, which are lines through opposite vertices, and the four lines of symmetry are formed by lines through the midpoints of opposite sides. Thus, a square has one vertical, one horizontal, and two diagonal symmetry lines.
Rectangle Line Symmetry
A rectangle has two symmetry lines, that is, lines that pass through the midpoints of opposing sides. When a rectangle is folded diagonally, the resulting shape is asymmetrical. Thus, a rectangle has only one vertical and one horizontal symmetry line.
Triangle Line Symmetry
A triangle’s line symmetry is determined by its sides. Scalene triangles lack line symmetry. If a triangle is isosceles, it has at least one line of symmetry; if it is equilateral, it has three.
Rhombus Line Symmetry
A rhombus has two symmetry lines. The rhombus’s two diagonals define its symmetry lines.
Circle Symmetry with Lines
Due to the fact that an endless number of lines can be drawn inside a circle that passes through its centre, a circle has an infinite number of symmetry lines.
Symmetry by Line Numbers
Three Lines of Symmetry
A triangle that is equilateral has approximately three lines of symmetry. Along its three medians, it is symmetrical.
Several additional patterns contain three lines of symmetry as well.
Four Lines of Symmetry
A square is symmetrical along four lines of symmetry, two diagonals, and two parallel to the opposing sides’ midpoints.
Several more patterns feature four lines of symmetry as well.
Five Lines of Symmetry
A regular pentagon is composed of approximately five lines of symmetry. The lines that connect a vertex to the opposing side’s midpoint divide the figure into ten symmetrical halves.
Other patterns, such as a star, also include five lines of symmetry.
Six Symmetrical Lines
A regular hexagon has six lines of symmetry, three connecting the opposite vertices and three connecting the opposite side’s mid-points.
Similarly, an N-sided regular polygon has N lines of symmetry.
Infinite Symmetry Lines
A circle can have an infinite number of symmetry lines or none at all. It is symmetrical in all directions.
Equation of Line Symmetry
A parabola has line symmetry in coordinate geometry, and its line of symmetry goes via its vertex. The line symmetry equation for a parabola with the quadratic equation y = ax2 + bx + c is of the form x = n, where n is a real number. The equation for the line of symmetry is x = -b/2a.
Examples of Lines of Symmetry
Below are some instances of the line of symmetry for various figures.
A triangle is said to contain three, one, or even no symmetry lines.
A quadrilateral has four, two, or no symmetry lines.
An Equilateral Triangle is considered to contain three symmetry lines.
The regular Pentagon has five symmetry lines.
A Regular Heptagon contains seven symmetry lines.
Conclusion
Symmetry is ingrained in geometry, nature, and shapes. It develops patterns that aid us in organizing our reality intellectually. We encounter symmetry on a daily basis yet are frequently unaware of it. Individuals work with symmetry ideas such as translations, rotations, reflections, and tessellations.
