Class 7 Maths - Symmetry

The following shape has rotational symmetry about the marked point of order:

When Fig is rotated through

$180^\circ$ , the image looks like the original. Thus, the given figure has rotational symmetry of order

$2$ about the marked point.

How many lines of symmetry are there in a regular hexagon?

A regular hexagon with six equal sides has six lines of symmetry.

For all regular polygons, the number of lines of symmetry is equal to the number of sides. That is an equilateral triangle has 3 lines of symmetry, a square has 4 lines of symmetry, similarly a regular hexagon has 6 lines of symmetry.

The answer is 6.

How many lines of symmetry are there in a regular octagon?

A regular octagon has 8 lines of symmetry.

The order of rotational symmetry about the marked point of the above shape is

If a figure is rotated by

$90^o$

$\Big(\dfrac{1}{4}^{th}$ of

$360^o \Big)$ ,then it exactly fits its own outline.

Therefore given figure has rotational symmetry of order

$4$ .

What is the order of rotational symmetry about the marked point?

When the figure is rotated by

$72^o$

$\Bigg(\dfrac{1}{5}^{th}$ of

$360^{o}\Bigg),$ then it exactly fits its own outline.

Therefore given figure has rotational symmetry of order

$5$ .

What is the order of rotational symmetry about the marked point?

Clearly, the image looks like the original after a rotation through

$360^\circ$ . Hence, it has rotational symmetry of order

$1$ .

Find the order of rotational symmetry
Refer above image.

The first :Its a plane shape.Its order is

$2$

The second: This shape has a reflectional symmetry. Its order is

$3$

The third: This shape has rotational symmetry since it looks the same after rotation.Its order is

$4$

Name the quadrilaterals which have both line and rotational symmetry of order more than $1$ .

Square is the quadrilateral which has both line and rotational symmetry of order more than

$1$ .

The no-of order of rotational symmetry of B, E, D?.

The rotational symmetry of in B,E,D is

of order 1. This is because we

get the same fig. after rotating

$360^{\circ}$

1120043_1202300_ans_88d4ef8e75d04c8bb53d32f0c6b55dae.jpg

Give the order of the rotational symmetry for above figure:

the order of the rotational symmetry of the figure is 2

1339476_1646594_ans_5974e723073245ea98178097e4c8934f.png

Can we have rotational symmetry of order more than $1$ whose angle of rotation is ${17}^{o}$

If the angle of rotation is

${17}^{o}$ , then symmetry of order is not possible because

${360}^{o}$ is not complete divided by

$17$

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

The given figure has its rotational symmetry as 5.After every rotation of

$72^{\circ}$ you will get same figure

ABCD is a parallelogram.
Write down the order of rotational symmetry of ABCD.

1) When parallelogram

$ABCD$ is rotated by

${ 180 }^{ 0 }$ , it fits onto itself.

2) Point

$A$ takes the place of point

$C$ , point

$B$ takes the place of point

$D$ , point

$C$ takes the place of point

$A$ and point

$D$ takes the place of point

$B$ .

3) When parallelogram

$ABCD$ is again rotated by

${ 180 }^{ 0 }$ , it regains its original position.

4) Thus, in a single turn of

$360^{ 0 }$ , parallelogram fits onto itself for two times. Thus, order of rotational symmetry of parallelogram is two.

Some english alphabets have fascinating symmetrical structures. From the following table, find the number of alphabets which have both the lines symmetry and rotational symmetry more than 1

Alphabets Line symmetry Number of lines symmetry Rotational symmetry Order of rotational symmetry
$Z$ No $0$ Yes $2$
$S$ No $0$ Yes $2$
$H$ Yes $2$ Yes $2$
$O$ Yes $2$ Yes $2$
$I$ Yes
$2$ Yes $2$
$N$ No $0$ Yes $2$
$C$ Yes $1$ No $1$

From the table, we can clearly see that

$H, O$ and

$I$ have both the lines symmetry and rotational symmetry as

$2$ .

In the word 'MATHS' which letter shows rotational symmetry of order $2$ ?

$\textbf{Step 1: Observe the letters to determine the required letter.}$

$\text{The given word is 'MATHS' .}$

$\text{The letters are 'M', 'A', 'T', 'H' and 'S' .}$

$\text{If a letter remains the same after a rotation of }$

$\mathrm{180^\circ}$

$\text{only, in clockwise or anti-clockwise direction,}$

$\text{then the letter has a rotational symmetry of order 2. }$

$\text{Observing the letters of the given word, we can say that, if we rotate the letter 'H' by }$

$\mathrm{180^\circ}$

$\text{in either direction, it will remain the same. }$

$\text{Thus, only 'H' shows rotational symmetry of order 2.}$

$\textbf{Hence, the required letter is 'H'.}$

2155090_1500679_ans_06e305bd78c748b996ebafd18fda31b8.png

Give the order the rotational symmetry for above figure:

1338869_1646598_ans_fccf0e6054254907aff73bdf86e9a6b7.png

After rotating by ${60}^{o}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Other angles will be

${12}^{o},{180}^{o},{240}^{o}, {300}^{o}, {360}^{o}$
1338886_1646609_ans_e8107359196e4852984c8308af3ae208.png

Give the order the rotational symmetry for above figure:

answer is given

1338863_1646593_ans_2411f0ba4702488a915ae1d7ef322a12.png

Give the order the rotational symmetry for the figure:

1338864_1646595_ans_37a85791d6fb43b399bed764a20b764d.png

Give the order the rotational symmetry for the above figure:

1338867_1646597_ans_f26e1de2611e43e6bd2632e8712198ea.png

Give the order the rotational symmetry for each figure:

1338871_1646599_ans_5048c4c7d9dd41e890bdc6fe1d59aaed.png

Give the order the rotational symmetry for each figure:

1338866_1646596_ans_f3c5e41bc4c64632a036e5ba9686705a.png

Give the order the rotational symmetry for each figure:

1338872_1646600_ans_ca96081e91bf4de9b9777b0492e6bdcf.png

State the number of lines of symmetry for regular pentagon:

A regular pentagon has

$5$ lines of symmetry.
1615556_1676570_ans_d60845e8a5ac4ada813091c67d415ad7.PNG

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

The given figure has its rotational symmetry as 3.After every rotation of

$120^{\circ}$ you will get same figure.

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

The given figure has its rotational symmetry as 2.After every rotation of

$180^{\circ}$ you will get same figure

Give the order of rotational symmetry for each of the following figure when rotated about the marked point $(x)$ :

The order of rotation will be 4. After every rotation of

$90^{\circ}$ you will get same figure.

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

We can see that three yellow lines which are at

$120^0$ each are lines of symmetry.

So, given figure has rotational lines of symmetry that is after moving figure by

$120^0$ we get same figure again.

1681479_1676711_ans_5781ccf419314f99b0b575ba38fccab2.png

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

The given figure has its rotational symmetry as 4.After every rotation of

$90^{\circ}$ you will get same figure

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

The given figure has its rotational symmetry as 4.After every rotation of

$90^{\circ}$ you will get same figure

What is the order of rotational symmetry of a square? Give the angles of such rotations.

Let us rotate a square ABCD (given in fig. 1) through

90o,180o,270o90o,180o,270o and

360o360o to attain the position shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5 respectively.
Clearly, each of the four times, the figure fits onto itself. 3, Fig. 4 and Fig. 5 respectively.
So, it has a rotational symmetry of order 4.

The number of lines of symmetry in a regular hexagon is _______ .

The number of lines of symmetry in a regular hexagon is

$6$ .

1647665_1790145_ans_4fbf0b7609ca4b60a0f7e6812b8644f0.png

Fill in the bank.
A regular polygon of n-sides has _____ number of lines of symmetry.

⇒ The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves.

⇒ The number of lines of symmetry in a regular polygon is equal to the number of sides.

Example: A triangle have 3 lines of symmetry and a square have 4.(Ref figure)

∴ Number of line symmetry of n sided regular polygon is n.

1708444_1809813_ans_116d848844ee4cb18c6cc6e9ca56e40f.PNG

The number of lines of symmetry in a regular polygon of n sided' is ________ .

The number of lines of symmetry in a regular polygon of n sided' is n.

If after a rotation of $45^{0}$ about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ________

If after a rotation of

$45^{0}$ about a fixed point the figure looks exactly the same, then the order of rotational symmetry is

$=\dfrac{360}{45}=8$ .

Find the number of lines of symmetry for the following shape:

There are

$6$ lines of symmetry for the given figure.

Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?

2 Lines of Symmetry

3 Lines of Symmetry

4 Lines of Symmetry

5 Lines of Symmetry

6 Lines of Symmery

8 Lines of Symmetry

7 Lines of Symmetry

The below figure has point symmetry.

Yes, there is implication between lines of symmetry and point symmetry.

On a squared paper, sketch the following : A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry on a squared paper, is shown in the above image.
1424747_1674911_ans_8195ada4153847848a2e9561b16e1b28.png

1424747_1674911_ans_8195ada4153847848a2e9561b16e1b28.png

Symmetry - Class 7 Maths - Extra Questions

The following shape has rotational symmetry about the marked point of order:

How many lines of symmetry are there in a regular hexagon?

How many lines of symmetry are there in a regular octagon?

The order of rotational symmetry about the marked point of the above shape is

What is the order of rotational symmetry about the marked point?

What is the order of rotational symmetry about the marked point?

Find the order of rotational symmetry
Refer above image.

Name the quadrilaterals which have both line and rotational symmetry of order more than $1$ .

The no-of order of rotational symmetry of B, E, D?.

Give the order of the rotational symmetry for above figure:

Can we have rotational symmetry of order more than $1$ whose angle of rotation is ${17}^{o}$

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

ABCD is a parallelogram.
Write down the order of rotational symmetry of ABCD.

In the word 'MATHS' which letter shows rotational symmetry of order $2$ ?

Give the order the rotational symmetry for above figure:

After rotating by ${60}^{o}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Give the order the rotational symmetry for above figure:

Give the order the rotational symmetry for the figure:

Give the order the rotational symmetry for the above figure:

Give the order the rotational symmetry for each figure:

Give the order the rotational symmetry for each figure:

Give the order the rotational symmetry for each figure:

State the number of lines of symmetry for regular pentagon:

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetry for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

What is the order of rotational symmetry of a square? Give the angles of such rotations.

The number of lines of symmetry in a regular hexagon is _______ .

Fill in the bank.
A regular polygon of n-sides has _____ number of lines of symmetry.

The number of lines of symmetry in a regular polygon of n sided' is ________ .

If after a rotation of $45^{0}$ about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ________

Find the number of lines of symmetry for the following shape:

Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?

On a squared paper, sketch the following : A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

Class 7 Maths Extra Questions

Alphabets	Line symmetry	Number of lines symmetry	Rotational symmetry	Order of rotational symmetry
$Z$	No	$0$	Yes	$2$
$S$	No	$0$	Yes	$2$
$H$	Yes	$2$	Yes	$2$
$O$	Yes	$2$	Yes	$2$
$I$	Yes	$2$	Yes	$2$
$N$	No	$0$	Yes	$2$
$C$	Yes	$1$	No	$1$

Symmetry - Class 7 Maths - Extra Questions

The following shape has rotational symmetry about the marked point of order:

How many lines of symmetry are there in a regular hexagon?

How many lines of symmetry are there in a regular octagon?

The order of rotational symmetry about the marked point of the above shape is

What is the order of rotational symmetry about the marked point?

What is the order of rotational symmetry about the marked point?

Find the order of rotational symmetry Refer above image.

Name the quadrilaterals which have both line and rotational symmetry of order more than 11.

The no-of order of rotational symmetry of B, E, D?.

Give the order of the rotational symmetry for above figure:

Can we have rotational symmetry of order more than 11 whose angle of rotation is 17o{17}^{o}

Give the order of rotational symmetric for each of the following figure when rotated about the marked point (x)(x):

ABCD is a parallelogram. Write down the order of rotational symmetry of ABCD.

In the word 'MATHS' which letter shows rotational symmetry of order 22?

Give the order the rotational symmetry for above figure:

After rotating by 60o{60}^{o} about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Give the order the rotational symmetry for above figure:

Give the order the rotational symmetry for the figure:

Give the order the rotational symmetry for the above figure:

Give the order the rotational symmetry for each figure:

Give the order the rotational symmetry for each figure:

Give the order the rotational symmetry for each figure:

State the number of lines of symmetry for regular pentagon:

Give the order of rotational symmetric for each of the following figure when rotated about the marked point (x)(x):

Give the order of rotational symmetric for each of the following figure when rotated about the marked point (x)(x):

Give the order of rotational symmetry for each of the following figure when rotated about the marked point (x)(x):

Give the order of rotational symmetric for each of the following figure when rotated about the marked point (x)(x):

Give the order of rotational symmetric for each of the following figure when rotated about the marked point (x)(x):

Give the order of rotational symmetric for each of the following figure when rotated about the marked point (x)(x):

What is the order of rotational symmetry of a square? Give the angles of such rotations.

The number of lines of symmetry in a regular hexagon is _______ .

Fill in the bank.A regular polygon of n-sides has _____ number of lines of symmetry.

The number of lines of symmetry in a regular polygon of n sided' is ________ .

If after a rotation of 45045^{0} about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ________

Find the number of lines of symmetry for the following shape:

Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry?

On a squared paper, sketch the following : A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

Class 7 Maths Extra Questions

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Find the order of rotational symmetry
Refer above image.

Name the quadrilaterals which have both line and rotational symmetry of order more than $1$ .

Can we have rotational symmetry of order more than $1$ whose angle of rotation is ${17}^{o}$

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

ABCD is a parallelogram.
Write down the order of rotational symmetry of ABCD.

In the word 'MATHS' which letter shows rotational symmetry of order $2$ ?

After rotating by ${60}^{o}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetry for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Give the order of rotational symmetric for each of the following figure when rotated about the marked point $(x)$ :

Fill in the bank.
A regular polygon of n-sides has _____ number of lines of symmetry.

If after a rotation of $45^{0}$ about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ________