# NCERT  Solutions for Class 7 Maths Exercise – 14 . 1  Chapter – 14 Symmetry

Q1. Copy the figures with punched holes and find the axes of symmetry for the following:

(a)

Solution:-

A figure has a line of symmetry, If there is a line about which the figure may be folded so that the two parts of the figure will coincide.

(b)

Solution:-

A figure has a line of symmetry , If there is a line about which the figure may be folded so that the two parts of the figure will coincide.

( c )

Solution:-

A figure has a line of symmetry If there is

a line about which the figure may be folded so that the two parts of the figure will coincide.

(d)

Solution:-

A figure has a line  of symmetry , If there is a line about which the figure may be folded so that the two parts of the figure will coincide.

( e )

Solution:-

A figure has a line of symmetry, If there is a line about which the figure may be folded so that the two parts of the figure will coincide.

(f)

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

(g)

Solution:-

A figure has a  line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figures will coincide.

(h)

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figures will coincide.

(i)

Solution:-

A figure has a line of symmetry, If there is a line about which the figure may be folded so that the two parts of the figures will coincide.

(j)

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

(k)

Solution:-

A figure ha s a line of symmetry , if there is a line about which the figure may be folded as that the two parts of the figures will coincide.

(l)

Solution:-

A figure has a line of symmetry , if there is a line about which the figures may be folded so that the two parts of the figures will coincide.

Q2. Given the line(s) of symmetry , find the other holes(s):

(a)

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, other hole is shown in the figure below.

(b)

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figures will coincide.

So, other hole is shown in the figure below.

( c )

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of figures will coincide.

So, other hole is shown in the figure below.

(d)

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

So, other hole is shown in the figure below.

( e )

Solution:-

A figure has a line of symmetry , If there is a line about which the figure may be folded so that the two parts of the figures will coincide.

So, other hole is shown in the figure below.

Q3. In the following figures, the mirror line is given as a dotted line. Complete each figures performing reflection in the dotted  line. . Are you able to recall the name of the figure you complete?

(a)

Solution:-

The concept of  line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps, visualise a line of symmetry .

While dealing with mirror reflection, care is needed to note down the the left – right changes in the orientation.

Name of the figure is square.

(b)

Solution:-

The concept of line of symmetry is closely related to the mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps  to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left – right chenges in the orientation.

Name of the figures is triangle.

( c )

Solution:-

The concept of  line of symmetry is closely related to the mirror reflection. A shape has line symmetry when one half of it is the mirror image  of the other half. A mirror line, thus helps to visualise a line of symmetry .

While dealing with mirror reflection,  care is needed to note down the left – right changes in the orientation.

Name of the figures is rhombus.

(d)

Solution:-

The concept of  line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry .

While dealing with mirror reflection care is needed to note down the left – right changes in the orientation.

Name of the figures is circle.

( e )

Solution:-

The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection care is needed to note down the left – right change sin the orientation.

Name of the figure is pentagon.

( f )

Solution:-

The concept of line of symmetry is closely related to the mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

Name of the figure is  octagon.

Q4. The following figures have more than  one line  of  symmetry . Such figures are said to have multiples lines of symmetry.

Identify multiples lines of symmetry , if any , in each of the  following figures:

(a)

Solution:-

Figures given has 3 lines of symmetry.

So, it has multiple lines of symmetry

(b)

Solution:-

Figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

( c )

Solution:-

Figure given has 3 lines of symmetry .

So, it has multiple lines of symmetry.

(d)

Solution:-

Figure given has 2 lines of symmetry

So, it has multiple lines of symmetry.

( e )

Solution:-

Figure given has 4 lines of symmetry.

So, it has multiple lines of  symmetry.

(f)

Solution:-

Figure given has only 1 line of symmetry.

(g)

Solution:-

Figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

(h)

Solution:-

Figure given has  6 lines of symmetry.

So, it has multiple lines of symmetry.

Q5. 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 figures be symmetric about both the diagonals ?

Solution:-

By observing the above figures,

Yes, the figures will be symmetrical about both diagonals.

By observing the above figures ,

Yes, the figure can be made symmetrical by more than one way.

Q6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):

(a)

Solution:-

The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image  of the other half. A mirror line, thus helps to visalise a line of symmetry.

While dealing with mirror reflection , care is needed to note down the left – right changes in the orientation.

(b)

Solution:-

The concept of line of symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection , care is needed to note down the left – right changes in the orientation

( c )

Solution:-

The concept of line  of symmetry is closely related to the mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half. A mirror line, thus helps to visualise a line of symmetry .

While dealing with mirror reflection, care is needed to  note down in the left – right changes in the orientation.

Q7. State the number of line of symmetry for the following figures:

• An equilateral triangle

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two partsof the figures will coincide.

In equilateral triangle has 3 lines of symmetry is shown in the figure below,

• An isosceles triangle

Solution:-

A figure has a line of symmetry if there is line about which the figure may be folded so that the two parts of the figures will coincide.

An isosceles triangle has 1 lines of symmetry is shown in the figure below,

( c ) A scalene triangle

Solution:-

A figure has a line of symmetry , if there is a  line about which the figure may be folded so that the  two parts of the figure will coincide.

A scalene triangle has no line of symmetry is shown in the figure below,

( d ) A square

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A square has 4 lines of symmetry is shown in the figure below,

( e ) A rectangle

Solution:-

A figure has a line of symmetry if there is  a line about which the figure may be folded so that  the two parts of the figures will coincide.

A rectangle has 2 lines of symmetry is shown in the figure below,

(f) A rhombus

Solution:-

A figure has a line of symmetry if there is a  line about which the figure may be folded so that the two parts of the figures will coincide.

A rhombus has 2 lines of symmetry is shown in the figure below,

(g) A parallelogram

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figures will coincide.

A parallelogram has no line of symmetry is shown in the figure below,

Solution:-

A figures has a line of symmetry If there is a line about which the figure may be folded so that the two parts of the figures will coincide.

A quadrilateral has no line of symmetry is shown in the figure below,

• A regular hexagon

Solution:-

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A regular hexagon has 6 lines of symmetry is shown in the figure below,

(j) A circle

Solution:-

A figure has a line of symmetry , if there is a line about which the figure may be folded so that the two parts of the figures will coincide.

A circle has infinite lines of symmetry.

Q8. What letters of the english alphabet have reflectional symmetry about.

• A vertical mirror (b) a horizontal mirror

( c ) both horizontal and vertical mirrors

Solution:-

• A vertical mirror

The English alphabet have reflection symmetry about a vertical mirror are , A , H , I , M , O ,T,U,V,X,Y,W

• A horizontal mirror

The English alphabet have reflection symmetry about a horizontal mirror are , B,C,D,E,H,I,K,O,X

( C ) Both horizontal and verticals mirrors

The English Alphabet have reflection symmetry about both horizontal and vertical mirrors are H,I,O,X

Q9. Give three examples of shapes with no line of symmetry.

Solution:-

A shape has no line of symmetry if there is no line about which the figure may be folded and also parts of the figure will not coincide.

A scalene triangle  a quadrilateral and a parallelogram

Q10. What other name you can give to the line of symmetry of (a) an isosceles triangle ?

Solution:-

The other name to the line of symmetry of an isosceles triangle is median or altitude.

• A Circle ?

Solution:-

The other name to the line of symmetry of a circle is diameter.

NCERT solutions for class 7 science chapter 11

NCERT  Solutions for Class 7 Maths Exercise – 14 . 1  Chapter – 14 Symmetry Q1. Copy the figures with punched…