In the realm of Mathematics, symmetry is a fundamental concept that possesses both aesthetic and practical applications. Symmetry is a property that indicates a perfect balance and proportionate similarity found in two halves of an object. A symmetrical object exudes a sense of harmony and order, which can be visually pleasing and structurally advantageous.
What is Symmetry?
Symmetry, in its simplest form, can be understood as a balanced and proportionate similarity found in two halves of an object. If an object can be divided into two identical halves, it is said to exhibit symmetry. This means that one-half is the mirror image of the other half. Symmetry can be found in an array of elements in our daily lives, from architecture and art to nature and even our own bodies.
What is the Line of Symmetry?
The line of symmetry, often referred to as the axis of symmetry or mirror line, is an imaginary line that bisects an object into two identical halves. The line passes through the center of the object and divides it in such a way that one side of the object is a mirror reflection of the other. Thus, the line of symmetry serves as the mirror line and presents two reflections of an image with the same dimensions that coincide, hence giving rise to the term ‘reflection symmetry’.
Types of Line of Symmetry
Vertical Line of Symmetry
The vertical line of symmetry is a standing straight line that bisects a geometric shape into two equal halves in a top-to-bottom or bottom-to-top manner. This line creates two mirror halves that are identical when viewed from a vertical or upright position.
Horizontal Line of Symmetry
The horizontal line of symmetry, on the other hand, is a sleeping straight line that bisects a geometric shape into two equal halves in a side-to-side manner. This line of symmetry divides a shape into identical halves when cut from right to left or vice-versa.
Three Lines of Symmetry
An equilateral triangle exemplifies a shape with three lines of symmetry. The triangle is symmetrical along its three medians, creating three equal and symmetrical sections.
Four Lines of Symmetry
A square, for instance, is symmetrical along four lines of symmetry – two along the diagonals and two along the midpoints of the opposite sides.
Five Lines of Symmetry
A regular pentagon is an example of a shape with five lines of symmetry. The lines joining a vertex to the midpoint of the opposite side divide the figure into ten symmetrical halves.
Six Lines of Symmetry
A regular hexagon exemplifies a shape with six lines of symmetry. Three of these lines join the opposite vertices, and the other three join the midpoints of the opposite sides.
Infinite Lines of Symmetry
A circle is an example of a shape with infinite or countless lines of symmetry. The circle is symmetrical along all its diameters, which can be infinitely drawn.
Diagonal Line of Symmetry
The diagonal line of symmetry is a slanted line that bisects a geometric shape into two equal halves in a diagonal manner. This line of symmetry divides a shape into identical halves when split across the diagonal corners.
Line of Symmetry in Shapes
Line Symmetry in Square
A square has four lines of symmetry. These lines pass through the opposite vertices, and the lines through the midpoints of opposite sides make up the four lines of symmetry. So, a square has one vertical, one horizontal, and two diagonal lines of symmetry.
Line Symmetry in Rectangle
A rectangle, on the other hand, has two lines of symmetry. These lines pass through the midpoints of opposite sides. When a rectangle is folded along its diagonals, the shape is not symmetrical. So, a rectangle has just one vertical and one horizontal line of symmetry.
Line Symmetry in Triangle
The line symmetry in a triangle depends upon its sides. If a triangle is scalene, then it has no line symmetry. If a triangle is isosceles, then it has at least one line of symmetry, and if the triangle is equilateral, then it has three lines of symmetry.
Line Symmetry in Circle
Since an infinite number of lines can be drawn inside a circle passing through its center, therefore a circle has an infinite number of lines of symmetry.
Lines of Symmetry in Quadrilateral
Quadrilateral is a polygon which has four sides. The different types of quadrilateral are trapezium, parallelogram, rhombus, square, rectangle, and kite. Let’s learn about the symmetry lines in different Quadrilateral.
Lines of Symmetry in Trapezium
A trapezium is a quadrilateral in which a pair of opposite sides are parallel. A Trapezium has no symmetry lines.
Lines of Symmetry in Parallelogram
A Parallelogram is a quadrilateral in which opposite sides are parallel and equal. A parllelogramn has no lines of symmetry.
Line of Symmetry in Kite
A kite contains one symmetry line. This symmetry line in kite is vertical in nature.
Lines of Symmetry in Rectangle
A rectangle has two symmetry lines: one vertical and one horizontal symmetry line. These lines pass through the midpoints of opposing sides. When it is folded diagonally, it gives asymmetrical shape.
Lines of Symmetry in Rhombus
A rhombus has two symmetry lines. These two lines of symmetry in rhombus are its diagonals.
Lines of Symmetry in Square
A square has four lines of symmetry: one vertical, one horizontal, and two diagonal symmetry lines. The four lines of symmetry are formed by lines through the midpoints of opposite sides.
Line Symmetry Equation
In the field of coordinate geometry, a parabola is a particular shape that exhibits line symmetry. For a parabola with a quadratic equation of the form y = ax^2 + bx + c, the equation of the line of symmetry is x = -b/2a. This formula allows us to calculate the axis of symmetry for any given parabola.
Solved Examples on Line of Symmetry
Now that we understand the concept of line symmetry let’s dive into some examples to further reinforce our understanding.
Example 1:
Write three capital letters in the English alphabet that have no lines of symmetry.
Solution:
The three capital letters in the English alphabet that have no lines of symmetry are P, G, and J.
Example 2:
Write three capital letters in the English alphabet with horizontal and vertical lines of symmetry.
Solution:
The three capital letters in the English alphabet that have both horizontal and vertical lines of symmetry are X, H, and O.
Example 3:
Write three capital letters in the English alphabet that have no lines of symmetry.
Solution:
The three capital letters in the English alphabet that have no lines of symmetry are P, G, and J.
How Kunduz Can Help You Learn Line of Symmetry?
Understanding symmetry, especially line symmetry, can be a challenging task. It requires a good grasp of geometric concepts, a sharp eye for detail, and a knack for visualizing shapes and patterns. Kunduz can help you master these skills with its expansive library of interactive games, fun worksheets, and comprehensive learning resources.
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