Symmetry - Class 7 Maths - Extra Questions

The following shape has rotational symmetry about the marked point of order:
426472.png

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.
592167_426472_ans.png


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.
470633_425375_ans.gif


The order of rotational symmetry about the marked point of the above shape is
426475_42a90b6b945848bba3b1e57aeb4a3849.png

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?

426478.png

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?
426477.png

Clearly, the image looks like the original after a rotation through $$360^\circ$$. Hence, it has rotational symmetry of order $$1$$.
592169_426477_ans.png


Find the order of rotational symmetry 
Refer above image.

1205534_00d6fb4125e449f190fea15fe3ddba85.png


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:
1646594_c430f6d73b2f4bd6b6d405d254b14f56.png

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 $$(x)$$:
1676706_840359c72ab549f5bffc1ed0c07a89d7.png

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.
1912934_90a5f700f3af445d80a4d3ca99b1aba8.png

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

AlphabetsLine symmetryNumber of lines symmetryRotational symmetryOrder 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:
1646598_669d5811d99249358f82c468a15f5849.png


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:
1646593_d251dd0d96f44cfb8ca70a206ca2080d.png

answer is given

1338863_1646593_ans_2411f0ba4702488a915ae1d7ef322a12.png


Give the order the rotational symmetry for the figure:
1646595_a875edf189e84135bafd6e5bc5b6515e.png


1338864_1646595_ans_37a85791d6fb43b399bed764a20b764d.png


Give the order the rotational symmetry for the above figure:
1646597_59f79301551a4b04bec392b0a1f42ce1.png


1338867_1646597_ans_f26e1de2611e43e6bd2632e8712198ea.png


Give the order the rotational symmetry for each figure:
1646599_37ac28dff2da49ce94c5c36ba629d731.png


1338871_1646599_ans_5048c4c7d9dd41e890bdc6fe1d59aaed.png


Give the order the rotational symmetry for each figure:
1646596_52026d50df9b4b12879751a8f03702f7.png


1338866_1646596_ans_f3c5e41bc4c64632a036e5ba9686705a.png


Give the order the rotational symmetry for each figure:
1646600_b8af2fc3392b49938e2263217f942bf2.png


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 $$(x)$$:
1676697_677e466e74ad4eaa92ef2679ea09d09b.png

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 $$(x)$$:
1676701_61e1730abadb4479a20244bf0c1359ae.png

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 $$(x)$$:
1676696_58867d04173a4d42bb286e6c0f306228.png

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 $$(x)$$:
1676711_fa12620aa80e44dd85d960e180f41f73.png

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 $$(x)$$:
1676700_eb1f8ae24d88420383b9f0b2eecb6e32.png

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 $$(x)$$:
1676704_877967b87d0043fb9d2d45940e43ef83.png

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:
1869827_3e52c11e784849d0bc3aa4a2d0f133df.png

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?
565015_90decc9900874cd5b95c8cfb860f1fdf.png

 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


Class 7 Maths Extra Questions