Symmetry  Class 7  Mathematics
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Exercise 12.1  Symmetry  NCERT  Mathematics  Class 7
Copy the figures with punched holes and find the axes of symmetry for the following:
Given the line(s) of symmetry, find the other hole(s):
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Sign up nowIn 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?
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Sign up nowThe following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
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Sign up nowCopy 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?
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Sign up nowCopy the diagram and complete each shape to be symmetric about the mirror line(s):
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Sign up nowState 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) Arectangle
(f) Arhombus
(g) A parallelogram
(h) A quadrilateral
(i) A regular hexagon
(j) A circle
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Sign up nowWhat 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
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Sign up nowGive three examples of shapes with no line of symmetry.
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Sign up nowWhat other name can you give to the line of symmetry of
(a) an isosceles triangle?
(b) a circle?
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Sign up nowExercise 12.2  Symmetry  NCERT  Mathematics  Class 7
Which of the following figures have rotational symmetry of order more than 1 :
a
Give the order of rotational symmetry for each figure:
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Sign up nowExercise 12.3  Symmetry  NCERT  Mathematics  Class 7
Name any two figures that have both line symmetry and rotational symmetry.
Two figures that have both line symmetry and rotational symmetry are:

Equilateral Triangle:
 Line Symmetry: An equilateral triangle has 3 lines of symmetry, each line reflecting through a vertex to the midpoint of the opposite side.
 Rotational Symmetry: It has a rotational symmetry of order 3, meaning you can rotate it by 120 degrees (360 degrees divided by 3) around its center and it will still look the same.

Square:
 Line Symmetry: A square has 4 lines of symmetry. Two lines are drawn through the center, connecting opposite vertices (diagonals) and two more connecting the midpoints of opposite sides.
 Rotational Symmetry: It has a rotational symmetry of order 4. You can rotate a square by 90 degrees (360 degrees divided by 4), 180 degrees, or 270 degrees around its center and it will appear unchanged.
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.
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Sign up nowIf a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1 ?
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Sign up nowFill in the blanks:
Shape  Centre of Rotation  Order of Rotation  Angle of Rotation 

Square  
Rectangle  
Rhombus  
Equilateral  
Equilateral Triangle  
Regular Hexagon  
Circle  
Semicircle 
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Sign up nowName the quadrilaterals which have both line and rotational symmetry of order more than 1 .
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Sign up nowAfter rotating by $60^{\circ}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
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Sign up nowCan we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) $45^{\circ}$ ?
(ii) $17^{\circ}$ ?
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