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Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
A scalene triangle, parallelogram, and a trapezium are three examples of shapes with no line of symmetry.
- 2 min
- Lines of Symmetry of Triangles
- Lines of Symmetry of A Square
- Lines of Symmetry of A Rectangle
- Lines of Symmetry of A Rhombus
- Lines of Symmetry of A Parallelogram
- Lines of Symmetry of A Kite
- Lines of Symmetry on A Trapezium
- Lines of Symmetry of A Pentagon
- Lines of Symmetry of A Hexagon
- Lines of Symmetry on An Octagon
Equilateral triangles have 3 lines of symmetry, which each pass through each corner to the middle of the opposite side. Isosceles triangles have 1 line of symmetry, which is directly between the two equal sides and equal angles. Scalene triangles have no equal sides and so, they have no lines of symmetry.
A square has 4 lines of symmetry. There are 2 lines of symmetry passing from each corner to the opposite corner. There are a further 2 lines of symmetry passing through the middle of each side to the middle of the opposite side.
A rectangle has 2 lines of symmetry. These lines pass from the middle of each side to the middle of the opposite side. There are no lines of symmetry passing through the diagonals of the rectangle. The diagonals of a rectangle are not lines of symmetry. We can see that the diagonals of a rectangle are not lines of symmetry.
A rhombus has 2 lines of symmetry. These lines of symmetry pass through the diagonals of the rhombus, from each corner to the opposite corner. Here are the 2 lines of symmetry of a rhombus.
A parallelogram has 0 lines of symmetry. This is because the diagonals of a parallelogram are not symmetrical. If we fold a parallelogram along its diagonals, it will not fold exactly in half without overlap.
Every kite has one line of symmetry. This line of symmetry passes vertically down the centre of the kite.
Trapeziums have no lines of symmetry unless they are isosceles trapeziums which have 1 line of symmetry. This means that a trapezium only has a line of symmetry if both of its diagonal sides are the same length. In this case, the line of symmetry passes directly between the 2 diagonal sides.
A regular pentagon has 5 lines of symmetry. Each line of symmetry passes from each of the 5 corners, through the centre of the pentagon to the middle of the opposite side. Here are the 5 lines of symmetry shown on a regular pentagon.
A regular hexagon has 6 lines of symmetry. 3 lines of symmetry pass from each of the corners to the opposite corner. The other 3 lines of symmetry pass from the middle of each side to the middle of the opposite side. Here are the lines of symmetry of a regular hexagon.
A regular octagon has 8 lines of symmetry. 4 lines of symmetry pass from each of the corners to the opposite corner. The other 4 lines of symmetry pass from the middle of each side to the middle of the opposite side. Here are the lines of symmetry on a regular octagon.
The shapes or objects that are irregular and do not resemble each other when divided into two parts are called ASYMMETRIC. Such shapes do not have a line of symmetry. A scalene triangle, a parallelogram, and a trapezium are examples of shapes that have no lines of symmetry.
1. Symmetry of a Line: A line has indefinite length and it can be considered that each line perpendicular to the given line divides the line into two equal halves. So a line has infinite symmetrical lines which are perpendicular to it. Also a line is symmetrical to itself. 2. Symmetry of a Line Segment:
Look at the following pictures and observe. Observe that for each of the above figures, the one half on one side of the dotted line is exactly identical to the one half on the other side of the dotted line. When we fold these figures along the dotted line, one half of the figure would fit exactly over the other half.
Lines of symmetry are straight lines that divide a shape into two equal parts where one part is an exact reflection of the other. E.g. A rectangle has two lines of symmetry (LoS) shown below using a dashed line.
