line symmetry

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.

Intuitive Notion of Line Symmetry and Plane Symmetry

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Intuitive Notion of Line Symmetry and Plane Symmetry

Line symmetry

Line symmetry, or just symmetry, occurs when two halves of a figure mirror each other across a line. The line of symmetry is the line that divides the figure into two mirror images. A simple test to determine if a figure has line symmetry is to fold the figure along the supposed line of symmetry and see if the two halves of the figure coincide.

A figure in the plane has a line of symmetry if the figure can be mapped onto itself by a reflection in the line.

  1. Nature displays line symmetry in some of its most beautiful work. The balanced arrangement of symmetry creates pleasing and attractive forms.
    Intuitive Notion of Line Symmetry and Plane Symmetry 1The white line is the line of symmetry.
  2. Many flowers possess line symmetry. The biologist’s term for line symmetry is “bilateral symmetry.”
    Intuitive Notion of Line Symmetry and Plane Symmetry 2The black lines are the line of symmetry.
  3. Mosaics and art work often demonstrate the concept of reflections and line symmetry. This drawing has two lines of symmetry, as shown by the white lines.
    Intuitive Notion of Line Symmetry and Plane Symmetry 3
  4. This butterfly caterpillar displays line symmetry.
    Intuitive Notion of Line Symmetry and Plane Symmetry 4The pink line is the line of symmetry.
  5. Certain letters of the alphabet and words possess line symmetry (such as the samples in the photo).
    Intuitive Notion of Line Symmetry and Plane Symmetry 5Notice that some letters possess vertical line symmetry, some possess horizontal line symmetry, and some possess BOTH vertical and horizontal line symmetry.
  6. Certain geometric figures possess line symmetry. The figures in the photo are only a sampling of the geometric figures which possess symmetry.
    Intuitive Notion of Line Symmetry and Plane Symmetry 6

Plane symmetry

Plane symmetry occurs when a plane intersects a three dimensional figure such that one half is the reflected image of the other half. Such a plane is imaginary and divides an object into two halves, each of which is the mirror image of the other in this plane.

Plane symmetry is analogous to line symmetry, only in three dimensions. Common objects displaying plane symmetry are rectangular solids, spheres, boxes, cones, and humans.
Intuitive Notion of Line Symmetry and Plane Symmetry 7Intuitive Notion of Line Symmetry and Plane Symmetry 8

Doctors repair damaged human faces by reconstructing the symmetry plane of the former healthy face from the damaged asymmetrical patient’s face.

Definition: A set of points has line symmetry if and only if there is a line, l, such that the reflection through l of each point of the set is also a point of the set.
Intuitive Notion of Line Symmetry and Plane Symmetry 9