NCERT MATHS CLASS 7 गणित कक्षा 7
Chapter 14 Symmetry
अध्याय 14 सममिति
LINK TO SOLUTIONS OF ALL QUESTIONS IS GIVEN BELOW
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ALL ABOUT SEMMETRY
1. A figure has line symmetry, if there is a line about which the figure may be folded so
that the two parts of the figure will coincide.
2. Regular polygons have equal sides and equal angles. They have multiple (i.e., more
than one) lines of symmetry.
3. Each regular polygon has as many lines of symmetry as it has sides.
Regular Regular Regular Square Equilateral
Polygon hexagon pentagon triangle
Number of lines 6 5 4 3
of symmetry
4. Mirror reflection leads to symmetry, under which the left-right orientation have to be
taken care of.
5. Rotation turns an object about a fixed point.
This fixed point is the centre of rotation.
The angle by which the object rotates is the angle of rotation.
A half-turn means rotation by 180o
; a quarter-turn means rotation by 90o
. Rotation
may be clockwise or anticlockwise.
6. If, after a rotation, an object looks exactly the same, we say that it has a rotational
symmetry.
7. In a complete turn (of 360o
), the number of times an object looks exactly the same is
called the order of rotational symmetry. The order of symmetry of a square, for
example, is 4 while, for an equilateral triangle, it is 3.
8. Some shapes have only one line of symmetry, like the letter E; some have only rotational
symmetry, like the letter S; and some have both symmetries like the letter H.
The study of symmetry is important because of its frequent use in day-to-day life and
more because of the beautiful designs it can provide us.
EXERCISE 14.1
1. Copy the figures with punched holes and find the axes of symmetry for the following:
2. Given the line(s) of symmetry, find the other hole(s)
3. In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted
line. Complete each figure performing reflection in the dotted (mirror) line. (You might
perhaps place a mirror along the dotted line and look into the mirror for the image).
Are you able to recall the name of the figure you complete?
4. The following figures have more than one line of symmetry. Such figures are said to
have multiple lines of symmetry.
Identify multiple lines of symmetry, if any, in each of the following figures:
5. Copy the figure given here.
Take any one diagonal as a line of symmetry and shade a few more squares to make
the figure symmetric about a diagonal. Is there more than one way to do that? Will
the figure be symmetric about both the diagonals?
6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):
7. State the number of lines of symmetry for the following figures:
(a) An equilateral triangle (b) An isosceles triangle (c) A scalene triangle
(d) A square (e) A rectangle (f) A rhombus
(g) A parallelogram (h) A quadrilateral (i) A regular hexagon
(j) A circle
8. What letters of the English alphabet have reflectional symmetry (i.e., symmetry related
to mirror reflection) about.
(a) a vertical mirror (b) a horizontal mirror
(c) both horizontal and vertical mirrors
9. Give three examples of shapes with no line of symmetry.
10. What other name can you give to the line of symmetry of
(a) an isosceles triangle? (b) a circle?
EXERCISE14.2
1. Which of the following figures have rotational symmetry of order more than 1:
(a) (b) (c) (d) (e) (f)
2. Give the order of rotational symmetry for each figure:
EXERCISE 14.3
1. Name any two figures that have both line symmetry and rotational symmetry.
2. Draw, wherever possible, a rough sketch of
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only line symmetry and no rotational symmetry of order more
than 1.
(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line
symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
3. If a figure has two or more lines of symmetry, should it have rotational symmetry of
order more than 1?
4. Fill in the blanks:
5. Name the quadrilaterals which have both line and rotational symmetry of order more
than 1.
6. After rotating by 60° about a centre, a figure looks exactly the same as its original
position. At what other angles will this happen for the figure?
7. Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°? (ii) 17°?
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