7th Class Mathematics Symmetry

Symmetry

Category : 7th Class

 Symmetry


  • Linear symmetry: If a line divides a given figure into two coinciding parts, we say that the figure is symmetrical about the line and the line is called the axis of symmetry or line of symmetry.

 

 

                       

 

 

  • A line of symmetry is also called a mirror line.
  • A figure may have no line of symmetry, only one line of symmetry, two lines of symmetry or multiple lines of symmetry.
  • Regular polygons have equal sides and equal angles. They have multiple lines of symmetry.
  • Each regular polygon has as many lines of symmetry as its sides.
  • A scalene triangle has no line of symmetry.
  • A parallelogram has no line of symmetry.
  • A line segment is symmetrical about its perpendicular bisector.
  • An angle with equal arms has one line of \[\leftrightarrow \]symmetry.
  • An isosceles triangle has one line of symmetry.
  • An isosceles trapezium has one line of symmetry.
  • A semicircle has one line of symmetry.
  • A kite has one line of symmetry.
  • A rectangle has two lines of symmetry.
  • A rhombus has two lines of symmetry.
  • An equilateral triangle has three lines of symmetry
  • A square has four lines of symmetry.
  • A circle has an infinite number of lines of symmetry.
  • In English alphabet, the letters A, B, C, D, E, K, M, T, U, V, W and Y have one line of symmetry and the letters H, I, X have two lines of symmetry
  • In English alphabet, the letters F, GJ, L, N, P, Q, R, S and Z have no line of symmetry The letter 0 has many lines of symmetry.

 

  • The line symmetry is closely related to mirror reflection. When dealing with mirror reflection, we have to take into account the left\[\leftrightarrow \] right changes in orientation.
  • Point symmetry: A figure is said to be symmetric about a point 0, called the centre of symmetry, if corresponding to each point P on the figure, there exists a point P' on the other side of the centre, which is exactly opposite to the point P and lies on the figure.

 

            Note:    A figure that possesses a possesses a point symmetry, regains its original shape even after beging rotated through \[\mathbf{18}{{\mathbf{0}}^{\mathbf{o}}}\]

                       

 

Letters of the English alphabet

Line of symmetry

A,M,T,U,V,W and Y

Vertical

B,C,D,E and K

Horizontal

H,I and X

Both  vertical and horizontal

F,G,J,L,N,P,Q,R,S and Z

None

O

 Infinitely many

 

  • Rotational symmetry: A figure is said to have rotational symmetry if it fits onto itself more than once during a complete rotation.
  • The number of times a figure fits onto itself in one complete rotation is called the order of
  • Rotational symmetry.
  • A line segment AB possesses a rotational symmetry of order 2 about the midpoint 0 of the line segment.
  • An equilateral triangle ABC possesses a rotational symmetry of order 3 about the point of intersection 0 of the bisectors of the interior angles.
  • A square ABCD possesses a rotational symmetry of order 4 about the point of intersection 0 of its diagonals.
  • A rhombus ABCD possesses a rotational symmetry of order 2 about the point of intersection 0 of its diagonals.

 

  • A rectangle ABCD possesses a rotational symmetry of order 2 about the point of intersection 0 of its diagonals.

 

  • A parallelogram ABCD possesses a rotational symmetry of order 2 about the point of intersection 0 of its diagonals.

 

  • A regular pentagon possesses a rotational symmetry of order 5 about the point of intersection 0 of the perpendicular bisectors of the sides of the pentagon.
  • A regular hexagon possesses a rotational symmetry of order 6 about the centre 0 of the hexagon.
  • A circle with centre 0 possesses a rotational symmetry of an infinite order about the centre 0.
  • The following letters of the English alphabet have rotational symmetry about the point marked on them.

 

 

Other Topics

Notes - Symmetry
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