**NCERT** Solutions for Class 7 Maths Chapter 14 Symmetry contains the answers to all the questions present in the textbook of NCERT. These Solutions for Class 7 Maths is an essential study material as it offers a wide range of questions that test the students’ understanding of concepts. A downloadable FREE PDF is available for Class 7 Chapter-14 Symmetry. Chapter 14 – Symmetry contains 3 exercises, and the NCERT Solutions for Class 7 Maths is available below.

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## NCERT Solutions for Class 7 Maths Chapter 14 Symmetry: EX 14.1 PDF

**Question 1.**

**Copy the figures with punched holes and find the axes of symmetry for the**

**following:**

(a)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(b)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(c)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(d)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(e)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(f)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(g)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(h)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(i)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(j)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(k)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

(l)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

**Question 2.**

**Given the line(s) of symmetry, find the other hole(s):**

(a)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, below is the required figure with other hole.

(b)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, below is the required figure with other hole.

(c)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, below is the required figure with other hole.

(d)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, below is the required figure with other hole.

(e)

**Solution**:-

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, below is the required figure with other hole.

**Question 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?**

(a)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

The given figure is square.

(b)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

The given figure is triangle.

(c)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

The given figure is rhombus.

(d)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

The given figure is circle.

(e)

**Solution:-**

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

The given figure is pentagon.

(f)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

The given figure is octagon.

**Question 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:**

(a)

**Solution**:-

The given figure contains 3 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

(b)

**Solution**:-

The given figure contains 2 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

(c)

**Solution**:-

The given figure contains 3 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

(d)

**Solution**:-

The given figure contains 2 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

(e)

**Solution**:-

The given figure contains 4 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

(f)

**Solution**:-

The given figure contains only 1 line of symmetry.

(g)

**Solution**:-

The given figure contains 4 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

(h)

**Solution**:-

The given figure contains 6 lines of symmetry.

Therefore, it is a case of multiple lines of symmetry.

**Question 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?**

**Solution**:-

From the given figure it can be observed that,

Yes, it symmetrical about both diagonals.

From the given figure it can be observed that,

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

**Question 6.**

**Copy the diagram and complete each shape to be symmetric about the**

**mirror line(s):**

(a)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

(b)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

(c)

**Solution**:-

Mirror reflection closely relates to the concept of line of symmetry.

A shape can be called if it has line symmetry when one half of it is the mirror image of the other half.

Therefore, a mirror line, can help to visualise a line of symmetry.

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

**Question 7.**

**State the number of lines of symmetry for the following figures:**

**(a) An equilateral triangle**

**(b) An isosceles triangle**

**(c) Scalene triangle**

**(d) A square**

**(e) A rectangle**

**(f) A rhombus**

**(g) A parallelogram**

**(h) A quadrilateral**

**(i) A regular hexagon**

**(j) A circle**

**Solution**:-

(a) An equilateral triangle

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, an equilateral triangle contains 3 lines of symmetry that is shown in the figure below,

(b) An isosceles triangle

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, an isosceles triangle contains 1 lines of symmetry as shown in the figure below,

(c) Scalene triangle

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a scalene triangle has no line of symmetry as shown in the figure below,

(d) A square

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a square has a total 4 lines of symmetry as shown in the figure below,

(e)

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a rectangle has a total 2 lines of symmetry as shown in the figure below,

(f)

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a rhombus has a total 2 lines of symmetry as shown in the figure below,

(g) A parallelogram

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a parallelogram has no line of symmetry as shown in the figure below,

(h) A quadrilateral

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a quadrilateral has no line of symmetry as shown in the figure below,

(i) A regular hexagon

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

So, a regular hexagon has a total 6 lines of symmetry as shown in the figure below,

(j) A circle

The given figure has ‘Line Symmetry’ i.e. if the figure is folded with the given line then the two parts of the figure will coincide.

A circle can have infinite lines of symmetry,

**Question 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**

**Solution:-**

(a) A vertical mirror

The English alphabet that has reflection symmetry with a vertical mirror are,

A, H, I, M, O, T, U, V, W, X, Y

(b) A horizontal mirror

The English alphabet that has reflection symmetry with a horizontal mirror are,

B, C, D, E, H, I, K, O, X

(c) both horizontal and vertical mirrors

The English alphabet that has reflection symmetry with both horizontal and vertical mirrors are, H, I, O, X

**Question 9.**

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

**Solution**:-

A shape contains a no line of symmetry,

If there is no line about which the figure can be folded and also parts of the figure will not coincide.

So, a scalene triangle, a quadrilateral and a parallelogram are the examples.

**Question 10.**

**What other name can you give to the line of symmetry of**

**(a) an isosceles triangle?**

**(b) a circle?**

**Solution**:-

(a)

The other name that can be given to line of symmetry of an isosceles triangle is median or altitude.

(b)

The other name that can be given to line of symmetry of a circle is diameter.

## NCERT Solutions for Class 7 Maths Chapter 14 Symmetry: EX 14.2 PDF

**Question 1.**

**Which of the following figures have rational symmetry of order more than**

**1:**

**Solution**:-

(a)

Therefore, from the pattern it can be visualised that it has rotational symmetry as 4.

(b)

Therefore, from the pattern it can be visualised that it has rotational symmetry as 3.

(c) It has only one rotational symmetry.

(d)

Therefore, from the pattern it can be visualised that it has rotational symmetry as 2.

(e)

Therefore, from the pattern it can be visualised that it has rotational symmetry as 3.

(f)

Therefore, from the pattern it can be visualised that it has rotational symmetry as 4.

So by observing all the figures

(a), (b), (c), (d), (e) and (f) have rotational symmetry of order more than 1.

**Question 2.**

**Give the order of rotational symmetry for each figure:**

(a)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 2.

(b)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 2.

(c)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 3.

(d)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 4.

(e)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 4.

(f)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 5.

(g)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 6.

(h)

**Solution**:-

Therefore, from the pattern it can be visualised that it has rotational symmetry as 3.

## NCERT Solutions for Class 7 Maths Chapter 14 Symmetry: EX 14.3 PDF

**Question 1.**

**Name any two figures that have both line symmetry and rotational**

**symmetry.**

**Solution**:-

The two figures are

Equilateral triangle

Circle.

**Question 2.**

**Draw, wherever possible, a rough sketch of**

**(i) a triangle with both line and rotational symmetries of order more than**

**1.**

**Solution**:-

A triangle that has both line as well as rotational symmetries of order more than 1 is an equilateral triangle.

Line symmetry

Rotational symmetry

**(ii) a triangle with only line symmetry and no rotational symmetry of order**

**more than 1.**

**Solution**:-

A triangle that has only line symmetry and no rotational symmetry of order more than 1 is isosceles triangle.

(iii) a quadrilateral with a rotational symmetry of order more than 1 but

not a line symmetry.

**Solution**:-

So, a quadrilateral that has a rotational symmetry of order more than 1 but does not show a line symmetry is not possible.

A quadrilateral with line symmetry may have rotational symmetry of order one but not more than 1.

(iv) a quadrilateral with line symmetry but not a rotational symmetry of

order more than 1.

**Solution**:-

Rhombus is quadrilateral that has a line symmetry but not a rotational symmetry of order more than 1.

**Question 3.**

**If a figure has two or more lines of symmetry, should it have rotational**

**symmetry of order more than 1?**

**Solution**:-

Yes. If a figure contains two or more lines of symmetry,

So it will have rotational symmetry of order more than 1

**Question 4.**

**Fill in the blanks:**

**Solution**:-

**Question 5.**

**Name the quadrilaterals which have both line and rotational symmetry of**

**order more than 1.**

**Solution**:-

The quadrilateral Square

Line symmetry:

Rotational symmetry:

**Question 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?**

**Solution**:-

The other angles in which the figure will look exactly the same are, 120°, 180°, 240°, 300°, 360°

So, the figure has rotational symmetry about same angle as the first one.

Therefore, the figure will look exactly the same when rotated by 60° from the last position.

**Question 7.**

**Can we have a rotational symmetry of order more than 1 whose angle of**

**rotation is**

**(i) 45°?**

**Solution**:-

Yes. A figure whose angle of rotation is 45o can have rotational symmetry of order more than 1.

**(ii) 17°?**

**Solution**:-

No. a figure cannot have a rotational symmetry of order more than 1 whose angle of rotation is 17o

.