(4-fold because there are 4 of them, that is,įour 90° rotational symmetry) The corners where any 4 squares meet, are also theĬenters of 2-fold rotational symmetries, each one being 180° rotational For example, if you rotate the chessīoard around any of the square's center by 90°, the pattern coincides again. For example, there are translational symmetries, because if you move the pattern up 2 squares or to the right 2 squares, the whole thing becomes itself again. (suppose the board is infinitely large so that the squares extends all ways on all sides) Suppose we have a checker-board, made up of alternating black and white squares. This topic is slightly complex, but let's take a look at a simple example - the checker-board. In a planar pattern (such as tilings, wallpapers, mosaics, Persian carpets), often there are many combinations of different symmetries in it. Glide-reflection symmetry are commonly found on the decorative patterns on vases or the edges of carpets. The right foot prints, are mirrored and moved, to match the left foot prints. The most obvious example of glide-reflectional symmetry is foot prints. Glide-Reflection SymmetryĪ glide-reflection symmetry is a combination of reflection symmetry and translation symmetry. (forward and backward here are counted as the same direction.) A brick wall, a tiled floor, chess-board, a honeycomb, all have translational symmetries in more than one directions. For example, rail-road track, staircase, ladder, all have translational symmetry in one direction. (this is because there is no evolutionaryĪdvantage to favor a particular side.) Translational SymmetryĪ translational symmetry is just the same pattern moved into a different location. Symmetry (along a horizontal line), and letters AHIMOTUVWXY have reflectional The capital letters BCDEKOX have reflectional The diamond ♦ has 2 reflectional symmetries The heart icon ♥, and other playing-card symbols the spade ♠, the club ♣ eachĪll have a reflectional symmetry. ☣, all have 3-fold (120°) rotational symmetry. The equal-sided triangle, or the radio active symbol ☢, or the bio-hazard symbol Other examples of 180° rotational symmetries includes the idealized letter shapes of The yin-yang symbol ☯ has a 180° rotational symmetry. Here are some examples of rotational symmetry: Let's look at some of the basic symmetries. Mathematicians have studied and analyzed symmetries, and have classified them into types. Now, in many floor tilings, wallpaper, or decorative patterns on vases, you'll see a pattern that repeats itself. If you look at staircase or brick walls, you'll notice that a pattern repeats again and again. A perfectly round O is symmetric around its center. The letter X is symmetric both horizontally and vertically. The letters B, C, D are the same along a horizontal line. Q.Ever notice, that some things are symmetric?įor example, the letters H, A, M, all look the same left and right.

Q.9 Give three examples of shapes with no line of symmetry.Q.7 State the number of lines of symmetry for the following figures:.

Q.6 Copy the diagram and complete each shape to be symmetric about the mirror line(s).

Is there more than one way to do that? Will the figure be symmetric about both the diagonals?

Q.5 Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal.

Identify multiple lines of symmetry, if any, in each of the following figures: Such figures are said to have multiple lines of symmetry.

Q.4 The following figures have more than one line of symmetry.

Are you able to recall the name of the figure you complete? (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Complete each figure performing reflection in the dotted (mirror) line.

Q.3 In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line.

Q.2 Give the line(s) of symmetry, find the other hole(s):.

Q.1 Copy the figures with punched holes and find the axes of symmetry for the following:.

NCERT solutions of related questions for Symmetry

Letters with reflection symmetry