Notes On Line Symmetry - CBSE Class 7 Maths

The word symmetry comes from the Greek word symmetros, which means even.
A figure has line symmetry if a line can be drawn dividing it into two identical parts. The line is called the line of symmetry or axis of symmetry.

Line symmetry is also known as reflection symmetry because a mirror line resembles the line of symmetry, where one half is the mirror image of the other half. While looking at a mirror, an object placed on the right appears to be on the left, and vice versa.

  • The line of symmetry of a line segment is its perpendicular bisector.
  • The lines of symmetry of an equilateral triangle are the bisectors of the internal angles.
  • The lines of symmetry of a square are the diagonals and the lines joining the mid-points of the opposite sides.
  • The lines of symmetry of a rectangle are the lines joining the mid-points of the opposite sides.
  • The lines of symmetry of a rhombus are the diagonals.
  • The line of symmetry of an isosceles triangle is the perpendicular bisector of the non-equal side.
  • A scalene triangle, has no line of symmetry.
  • A circle has unlimited lines of symmetry.


Lines of symmetry for regular polygons
A polygon is said to be a regular polygon if all its sides are equal in length and all its angles are equal in measure. If a polygon is not a regular polygon, then it is said to be an irregular polygon.

Regular and irregular polygons have lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides that it has. A regular pentagon has five lines of symmetry. Similarly, a regular octagon has eight lines of symmetry, while a regular decagon has ten lines of symmetry.

Lines of symmetry for Irregular polygons
Most irregular polygons do not have line symmetry. However, some of the irregular polygons have lines of symmetry. A rectangle has two lines of symmetry, and an isosceles triangle has one line of symmetry.

Lines of symmetry for letters
Some letters have line symmetry. The letters A, B, C, D, E, I, K, M, T, U, V, W and Y have one line of symmetry. The letters H and S have two lines of symmetry. The letters F, G, J, L, N, P, Q, R, S and Z have no line of symmetry.

Summary

The word symmetry comes from the Greek word symmetros, which means even.
A figure has line symmetry if a line can be drawn dividing it into two identical parts. The line is called the line of symmetry or axis of symmetry.

Line symmetry is also known as reflection symmetry because a mirror line resembles the line of symmetry, where one half is the mirror image of the other half. While looking at a mirror, an object placed on the right appears to be on the left, and vice versa.

  • The line of symmetry of a line segment is its perpendicular bisector.
  • The lines of symmetry of an equilateral triangle are the bisectors of the internal angles.
  • The lines of symmetry of a square are the diagonals and the lines joining the mid-points of the opposite sides.
  • The lines of symmetry of a rectangle are the lines joining the mid-points of the opposite sides.
  • The lines of symmetry of a rhombus are the diagonals.
  • The line of symmetry of an isosceles triangle is the perpendicular bisector of the non-equal side.
  • A scalene triangle, has no line of symmetry.
  • A circle has unlimited lines of symmetry.


Lines of symmetry for regular polygons
A polygon is said to be a regular polygon if all its sides are equal in length and all its angles are equal in measure. If a polygon is not a regular polygon, then it is said to be an irregular polygon.

Regular and irregular polygons have lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides that it has. A regular pentagon has five lines of symmetry. Similarly, a regular octagon has eight lines of symmetry, while a regular decagon has ten lines of symmetry.

Lines of symmetry for Irregular polygons
Most irregular polygons do not have line symmetry. However, some of the irregular polygons have lines of symmetry. A rectangle has two lines of symmetry, and an isosceles triangle has one line of symmetry.

Lines of symmetry for letters
Some letters have line symmetry. The letters A, B, C, D, E, I, K, M, T, U, V, W and Y have one line of symmetry. The letters H and S have two lines of symmetry. The letters F, G, J, L, N, P, Q, R, S and Z have no line of symmetry.

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