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How do you find Lines of Symmetry?

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How do you find Lines of Symmetry?

Line Symmetry  

A figure has a line symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide. All objects and all alphabets below figure have line symmetry.
How do you find Lines of Symmetry 1The concept of line symmetry is closely related to mirror reflection.
How do you find Lines of Symmetry 2Note :
If one half completely covers the other, we say that the line is the line of symmetry otherwise not.

Examples:

  1. Let PQRS be a kite in which PQ = PS and QR = SR.
    Then kite PQRS is symmetrical about diagonal PR.
    How do you find Lines of Symmetry 3
  2. A rectangle has two lines of symmetry, each one of which is the line joining the mid point of opposite sides.
    How do you find Lines of Symmetry 4
  3. A semicircle has one line of symmetry, namely the perpendicular bisector of diameter PQ.
    How do you find Lines of Symmetry 5
  4. A circle is symmetrical about each one of its diameters.
    How do you find Lines of Symmetry 6
  5. An equilateral triangle is symmetrical about each one of the bisectors of its interior angles.
    How do you find Lines of Symmetry 7
  6. A square has 4 lines of symmetry, namely the diagonals and lines joining the mid-points of its opposite sides.
    How do you find Lines of Symmetry 8
  7. A rhombus is symmetrical about each of its diagonals.
    How do you find Lines of Symmetry 9

Line of symmetry in regular polygons

Regular Polygon 
A closed figure bounded by straight line segments of equal length is called a Regular Polygon. For example, a square is a regular quadrilateral figure.
How do you find Lines of Symmetry 10Let us now discuss a method of finding lines of symmetry of a regular polygon.
1. An Equilateral Triangle
A triangle whose all sides are of same length and each of its angles measures 60°, is called an equilateral triangle shown in figure.
How do you find Lines of Symmetry 112. A Square
We have already discussed that a square is also a regular polygon because its all sides are of equal length and each of its angles is a right angle (of measure 90°) as in figure.
How do you find Lines of Symmetry 123. A Regular Pentagon
A figure bounded by five sides of equal length is called a regular pentagon. Each angle of a regular pentagon is 108°.
How do you find Lines of Symmetry 134. A Regular Hexagon
A figure bounded by six sides of equal length is called a regular hexagon. Each of its angle measures 120°.
How do you find Lines of Symmetry 14Trace an equilateral triangle on a tracing paper and find its lines of symmetry by folding.
How do you find Lines of Symmetry 15there are three lines of symmetry for an equilateral triangle.
Draw a square on a tracing paper.
How do you find Lines of Symmetry 16A square has four lines of symmetry.
How do you find Lines of Symmetry 17Note :

  1. We can also find the line of symmetry of a figure by putting a mirror. When the half part of a figure becomes same as its mirror image, we call the line along with mirror as the line of symmetry.
  2. In mirror reflection, the orientation of the figure changes into left-right orientation as shown in figure.

line symmetry Line of symmetry in regular polygons