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FOURTH GRADE / SYMMETRY 4.3 / ROTATIONAL SYMMETRY

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

  
WE WILL SEE THREE TYPES of SYMMETRIES:

 ♦ 
1- SYMMETRIES with respect to A LINE or PLANE .
 ♦ 2- TRANSLATIONAL SYMMETRY .
 ♦ 3- ROTATIONAL SYMMETRY .


THEY ARE REALLY of USE .
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1. In case of Rotational Symmetry, the shape or image can be rotated a definite amount and it looks the same.
On the way from the parking position in the garage to the road this wheel takes a distance of 10.5 m. If π is taken as 3, how many times has it got the same look (with respect to the Earth) ?

!
In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) 10
b) 15
c) 20
d) 30


One turn of the wheel means a distance of 2.1 m. is taken. But during one turn the wheel looks twice the same.
y
2. How many matches there are as you go once around is called the Order of (this particular) rotational symmetry.
The order of rotational symmetry of the following figure is 1. What will be the maximum order of symmetry of all possible forms the arms will generate within 12 hours ?

!
In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 0
b) 4
c) 1
d) 2
Rotational symmetry is space related. We have to turn the shape by a definite angle and should attain the same form as before rotation. Not anything should look different.
3. What is the order of rotational symmetry of the following figure ?

!
a) 8
b) 10
c) 12
d) 6
It's a dart board without numbers on .
4. What is the order of rotational symmetry of the following figure ?

!


a) 64
b) ∞
c) 32
d) 48
Just count a quarter of them .
5. What is the order of rotational symmetry of the following figure ?

!


a) 1
b) 4
c) 2
d) none
There is a small pase shift, look please carefully at . If the boundary were a circle, the shape would have an order a little bit grater than 1
6. What is the order of rotational symmetry of the following (blue) figure ?

!


a) 1
b) 0
c) ∞
d) 2
Do not try to count, it is a ring .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. The shapes are regular polygons. Which of the choices is the correctly ordered order of rotational symmetry ?

!
a) I, II and III
b) II, III and I
c) III, II and I
d) II , I and III
The rhombus is a square since it has right angles .
8. Written with "Times New Roman" font, which of the letters of the following figure has/have rotational symmetry ?

!
a) I
b) O
c) I and O
d) I, O and E
Look for the font via Google .
9. How many consonants of English, if written in capital form, do normally have rotational symmetry ?

a) 5
b) 7
c) 9
d) 10


There are 21 of them . Pay special attention to H, N, S, X and Z .
10. How many of the (arabic) digits display rotational symmetry ?

!


a) 1
b) 2
c) 3
d) 4
Only 0 and 8 .
11. What is the sum of the orders of rotational symmetries of all roman numerals shown below ?

!


a) 6
b) 10
c) 9
d) 12
Be careful, minimal order of rotational symmetry is not zero but 1 .
12. One of the implications of spherical symmetry is that the amount of flow changes inversely proportionally with the changing radius. The radii of the different colored spheres are 1, 2 and 3 units respectively. Their respective surface areas change proportionally with the radii and are , within the definite solid angle, A , 4xA and 9xA.
There is a spherical (point) source of light at the center of these spheres and the luminous fluxes (measure of the perceived power of light, measured in lumens) will then respectively be ... , (1/4)xL and (1/9)xL lumens at the surfaces of these spheres.

!


a) 1
b) 2xL
c) L/2
d) L
Do never forget the quantities and units, both of them, in case of physical quantities .
13. Which choice explains the meaning of the sentence "Charges on a spherical conductor display spherical symmetry." ?

!


a) charge is distributed
b) the amount of charges per unit area is the same everywhere
c) charge is distributed evrywhere
d) charge is localized
per unit area and ... .
14. Which of the traffic signs shown in the figure below has the greatest finite order of rotational symmetry ?

!


a) no entry
b) give way
c) prohibited road
d) priority road
Prohibited road has the highest but it is nor finite .
15. A pentomino is composed of five congruent squares, connected along their edges, shared edges overlapping completely . There are twelfe of them shown in the figure below.

!


Which of the pentominos has/have the greatest order of rotational symmetry ?

a) I
b) X
c) Z
d) N
The "X" pentomino is a cross and more symmetrical than our letter x .
16. What is the total order of rotational symmetry of 12 pentominos ?

a) 15
b) 17
c) 8
d) 12
The ones having no rotational symmetry have an order of 1 .
Z has a rotational symmetry of order 2.
I has a rotational symmetry of order 2.
X has a rotational symmetry of order 4.
17. An hexiamond (a special polyiamond) is a polyform whose base form is an equilateral triangle. It consists of 6 equilateral triangles having at least one common side. There are twelfe of them shown in the figure below.

!


Which of the hexiamonds has/have the greatest order of rotational symmetry ?

a) middle raw, first column
b) the I
c) the hexagonic one
d) upper raw, second column
One of them has an order of 6 .
18. What is the total order of rotational symmetry of 12 possible hexiamonds ?

a) 18
b) 12
c) 20
d) 30
One of them has 6, 3 of them has 2 .
19. How many type of symmetries does the figure below have and what is the order of rotational symmetry of it ?

!


a) 4
b) 1
c) 0
d) 2 and 2
It has 1st type of symmetry (w.r.t. a point and two lines) and rotational (3rd type) .
20. How is the figure of the previous question to be attained ?

a) via symmetries of a basic triangle
b) via symmetries
c) via a triangle
d) via rotation
Have please a look at the ry1 of question 22 if you can not guess .
21. How many type of symmetries does the figure below have and what is the order of rotational symmetry of it ?

!


a) 2 and 2
b) 2 and 4
c) 4 and 4
d) 4 and 1
It has 1st type of symmetry (w.r.t. a point and two lines) and rotational (3rd type) .
y
22. How is the figure of the previous question to be attained ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) via a basic triangle
b) via symmetries of a triangle
c) via symmetries
d) via rotations of a basic triangle


Have please a look at ry1.
23. Which of the followings have/has rotational symmetry ?

I- any polygon
II- a regular polygon
III- a line
IV- a plane

a) II and IV
b) I and II
c) I, II and IV
d) all
A plane has rotational symmetry .
24. Which of the followings have/has rotational symmetry (discrete or continuous) ?

I- a circle
II- a trapezoid
III- an hexagonal prism
IV- a tetrahedron

a) II
b) I
c) IV
d) III
Any circle has, no need for further thought .
25. What is the total order of rotational symmetry of the hexagons (incuding insides) in the figure ?

!


a) 6
b) 12
c) 2
d) ∞
One is totally excluded due to inside .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2011 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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