# 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.

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