What does symmetry (line symmetry) mean?

Any figure is said to have a line of symmetry, if on folding the figure about this line, the two parts of the figure exactly coincide.

s1If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror-image halves. Reference: https://www.learner.org

s2.jpgLine of symmetry of a Triangle: The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry.

  • A scalene triangle is a triangle with no lines of symmetry
  • Isosceles triangle has at least one line of symmetry and an
  • Equilateral triangle has three lines of symmetry.

Reference: https://www.illustrativemathematics.org


Line of symmetry of quadrilaterals:

  • The square has four lines of symmetry.
  • The rectangle has only two, as it can be folded in half horizontally or vertically.
  • The trapezoid has only a vertical line of symmetry.
  • The parallelogram has no line of symmetry.

Reference: https://www.illustrativemathematics.org

Line of symmetry of polygons:

  • A Regular Pentagon (5 sides) has 5 Lines of Symmetry.
  • A Regular Hexagon (6 sides) has 6 Lines of Symmetry.
  • A Regular Heptagon (7 sides) has 7 Lines of symmetry.
  • A Regular Octagon (8 sides)  has 8 Lines of Symmetry.

Reference: http://www.mathsisfun.com/

You can see the logic…. a polygon with n sides will have n  number of lines of symmetry.

Line of symmetry for other objects:

  • Kite shaped quadrilateral: This only have one line of symmetry.
  • Isosceles Trapezium: It has only one line of symmetry.
  • A semi-circle: It has only one line of symmetry.
  • A circle: It has infinite number of line of symmetry.
  • A line segment: It has two lines of symmetry. One is the perpendicular bisector and the other one is the line segment itself.
  • An angle: The angle has one line of symmetry. This is the angle bisector.
  • Letter A: It has one line of symmetry.
  • Letter H: It has two line of symmetry.

Properties of a line of symmetry:

  1. The figure on any side of the line of symmetry is a mirror image of the figure on the other side of it.
  2. A line of symmetry of a polygon is a perpendicular bisector of every line segment joining a pair of corresponding points of the polygon.
  3. In symmetric polygons, the corresponding sides and the corresponding angles are congruent.