Notes on Symmetry, Design and Tessellations | Grade 7 > Compulsory Maths > Symmetry, Design and Tesselation | KULLABS.COM

Symmetry, Design and Tessellations

  • Note
  • Things to remember
  • Videos
  • Exercise
  • Quiz

The dotted line which is the half part of each shape to one side of a dotted line is the mirror image of the other parts is called the line of symmetry . In another word, it is also called the axis of symmetry , so the figure is said to have bilateral symmetry or to be symmetrical by reflection in the dotted line and a line of symmetry shape can be turned so as it exactly into its outline.

Source : math.cmu.edu Fig :Symmetry
Source : math.cmu.edu
Fig :Symmetry

Rotational symmetry

When a shape can be mapped onto itself by a rotation of less than a complete turn (360o) about a point the shape is said to have a rotational symmetry .

Order of rotational symmetry

order of rotation
order of rotation

When the shape is rotated through a half -turn it can be fitted to the original shape . It means , when it is rotated through 2 times half-turns , it reaches its original position .

\(\therefore\) It has rotational symmetry of order 2.

When the equilateral triangle is rotated through a \(\frac{1}{3}\) of turn 120o, it can fit over the original shape. When it is rotated through3 times \(\frac{1}{3}\) and then it will reach its original place.

\(\therefore\) It has rotational symmetry of order 3.

When the square is rotated through quarter-turn \(\frac{1}{4}\)of the turn 90o. Which can be fitted over the original shape . It means when it is rotated through 4time \(\frac{1}{4}\)of turn , it reaches its original position .

\(\therefore\) It has rotational symmetry of order 4.

Tessellation

 mathworld.wolfram.com

A tessellation is known as tiling . It is covering of the plane with congruent geometrical shape un which a repeating pattern without leaving any gaps and without overlapping each other.The shape is polygons in it . It may be an equilateral triangle , regular hexagon or square . To make a tessellation :

  • We should not leave any gaps.
  • We should not have any overlaps.
  • We should use the sets of congruent figures .

Types of tessellation

  • Irregular tessellation : In this case , we use irregular types of polygons.
  • Semi-regular tessellations:In this case , we use two or more regular polygons . In the adjoining tessellation , regular octagons and squares are used .
  • Regular tesselation : In this case, we use the same types of regular polygons . The polygons that we use may be equilateral triangle, regular hexagon etc.



  • When the shape is rotated through a half -turn it can be fitted to the original shape .
  • To make a tessellation we should use the sets of congruent figures .
  • A tessellation is known as tiling . 
.

Very Short Questions

0%
  • The process of covering of the plane with congruent geometrical shapes in a repeating pattern without leaving any gaps and without overlapping each other is known as ______.

    tessellation
    graph
    design
    symmetry
  • Tessellation is also known as ______ .

    covering
    polygons
    gaps
    tiling
  • When a shape can be mapped into itself by a rotation of less than a complete turn around a point, the shape is said to be ______ .

    bilateral symmetry
    axis of symmetry
    line of symmetry 
    rotational symmetry 
  • Tessellation should not have any gaps and ______ .

    overlaps
    joint
    color
    order
  • Tessellation is done on the surface of floor and ______ .

    window
    door
    carpet
    cupboard
  • You scored /5


    Take test again

ASK ANY QUESTION ON Symmetry, Design and Tessellations

No discussion on this note yet. Be first to comment on this note