Free Symmetry Subjective Test 02 Practice Test - 7th grade

Question 1

How many lines of symmetry does a rectangle have? [1 MARK]

SOLUTION

Solution :
Two lines of symmetry are possible for a rectangle.

Question 2

Which of the following letters have vertical symmetry? Explain with reason. [2 MARKS]
A, C, E, H, S, V, Z

SOLUTION

Solution : Answer: 1 Mark
Reason: 1 Mark

Among the following letters only A, H and V have vertical symmetry.
A, H and V will look identical if we look at their images formed by a vertical mirror but the rest of the given letters won't.

Question 3

What is the order of rotational symmetry of an equilateral triangle? [2 MARKS]

SOLUTION

Solution :
Answer: 2 Marks

Rotate the given equilateral triangle about its centre to 120 degrees it looks the same.

If you rotate the given equilateral triangle by 120 degrees, 240 degrees,360 degrees it will be the same. Order of rotational symmetry is 3.

Question 4

A figure with an angle of rotation as $17^{\circ}$ has rotational symmetry of order more than 1. Is this statement correct or not and why? [2 MARKS]

SOLUTION

Solution :
Statement: 1 Marks
Reason: 1 Mark

The statement is not correct because $\frac{360}{17}$ is not a natural number, a figure can not have an angle of rotation as $17^{\circ}$ .

Question 5

How many lines of symmetry are present in a parallelogram? Include a diagram for reference. [2 MARKS]

SOLUTION

Solution :
Correct Answer: 1 Mark
Diagram: 1 Mark

A parallelogram has 0 lines of symmetry.

Question 6

Find the number of lines of symmetry for the following figure. [3 MARKS]

SOLUTION

Solution :
Answer: 1 Mark
Diagram: 1 Mark
Reason: 1 Mark

The figure has two lines of symmetry.

The lines joining the midpoints of the two sides will be the only lines of symmetry here.

Question 7

Given that the perimeter of a polygon is $92 m$ and its area is $529 m^{2}$ . Its adjacent sides are equal and perpendicular. Find the number of lines of symmetry.
[3 MARKS]

SOLUTION

Solution :
Process: 2 Marks
Result: 1 Mark

The given polygon is square.

Perimeter 4a = 92

a = 23 m

Area = $a^{2}$ = 529 $m^{2}$

Hence the above polygon is a square and a square has 4 lines of symmetry.

Question 8

Make the mirror image of the diagram and then make a final image after overlapping it on the mirror image. [3 MARKS]

SOLUTION

Solution :
Mirror image : 1 Mark
Final image : 2 Marks

The mirror image of the above diagram will be

On overlapping the original diagram on its mirror image, we get

Question 9

Find the number of lines of symmetry for the following figures.
(a)

(b)

[3 MARKS]

SOLUTION

Solution :
Answer: 1 Mark
Diagram with lines of symmetry: 2 Marks

(a) Number of line of symmetry in the figure is 1.

(b) The figure has 4 lines of symmetry.

Original Figure

Figure with lines of symmetry

Question 10

(a) Find the number of lines of symmetry of the following figure?

(b) How many angles of rotation will a regular polygon have if it has ‘n’ sides?
[4 MARKS]

SOLUTION

Solution :
(a) Answer : 1 Mark
Reason: 1 Mark
(b) Solution: 2 Marks

(a) The answer is 0.
When the line joining the midpoints of opposite sides divides the figure into two equal halves, such lines are called lines of symmetry. But the lines should not pass through the alphabets. Here no lines of symmetry are possible as no such line can be constructed which would divide the table without cutting through the alphabets.

(b) Angles of rotation of a regular polygon with ‘n’ sides = Y = n – 1

This is because the last rotation, i.e. $360^{\circ}$ is not counted as an angle of rotation. If it was counted as an angle of rotation, every object would have an angle of rotation.

So, angles of rotation for a square are $90^{\circ}$ , $180^{\circ}$ and $270^{\circ}$ . It’s only 3, not 4.

Question 11

(a) In a square, red balls are arranged along one diagonal and yellow balls are arranged along another diagonal. Find the rotational symmetry of the given arrangement?

(b) If ‘X’ is the order of rotation of a regular polygon with ‘n’ sides and ‘Y’ is the number of angles of rotation, what is the value of (X – Y – 1)? [4 MARKS]

SOLUTION

Solution :
(a) Diagram: 1 Mark
Reason: 1 Mark
(b) Solution: 2 Marks

(a) The answer is 2. The given diagram when rotated by 180 $^{o}$ and 360 $^{o}$ gives the same figure.

Due to different colours of the two diagonals, the figure won't look the same if it's rotated by 90 $^{o}$ or 270 $^{o}$ . Hence, it will have a rotational symmetry of only 2.

(b) Order of rotation of a regular polygon with ‘n’ sides = X = n

For e.g. an equilateral triangle and a square repeat the initial position 3 and 4 times respectively for $360^{\circ}$ rotation.

Angles of rotation of a regular polygon with ‘n’ sides = Y = n – 1

This is because the last rotation, i.e. $360^{\circ}$ is not counted as angle of rotation.

So, X – Y – 1 = n – (n – 1) – 1 = n – n + 1 – 1 = 0

Question 12

(a) A polygon has 2 lines of symmetry and order of rotational symmetry is 2. The adjacent sides of the polygon are not equal. The perimeter of the polygon is 24 m. Given one side length as 9 m, find the area of the polygon?

(b) The order of the rotational symmetry of the given figure about its centre is:

(c) The order of the rotational symmetry of the given figure about the point marked ‘x’ is:

[4 MARKS]

SOLUTION

Solution :
(a) Calculations: 1 Mark
Result: 1 Mark
(b) Answer: 1 Mark
(c) Answer: 1 Mark

(a) The given polygon will be a rectangle.

Perimeter = 24

2(a+b) = 24
Put a=9 [given]

b = 3

Area of the rectangle = (9)*(3)

= 27 $m^{2}$

(b) The number of positions in which the object looks exactly the same is called the order of rotational symmetry. The order of symmetry of the given figure is 2.

(c) The number of position in which the object look exactly the same is called the order of rotational symmetry. The order of symmetry of the given figure is 2.

Question 13

(a) Identify multiple lines of symmetry, if any, in the following figure:

(b) Sonali's brother drew the following pattern on a graph sheet. Can u determine if the pattern is symmetrical and if symmetrical, how many lines of symmetry are possible for the following figure?

[4 MARKS]

SOLUTION

Solution : Each part: 2 Marks

(a) The following figure will have 6 distinct lines which will cut the figure into identical halves.
Hence, it will have six lines of symmetry.

Lines of symmetry

(b) In the given figure, one line of symmetry is possible as depicted in the image below. By folding the figure about this line it will overlap completely.

Question 14

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

(b) Which kind of symmetry is illustrated in the image below?

[4 MARKS]

SOLUTION

Solution : (a) Exact figure: 2 Marks
(b) Correct answer: 2 Marks

(a)

(b) Line symmetry, mirror symmetry and reflection symmetry are nearly same.

If you fold the figure along the line representing the water level, then the lower half will perfectly align with the upper half. This means the water level is the line of symmetry. This happens because of reflection. The upper and lower halves cannot be different.

At conceptual level, there is no difference between line symmetry and mirror/reflection symmetry

Question 15

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

(b) Identify the multiple lines of symmetry, if any, in each of the following figures:

[4 MARKS]

SOLUTION

Solution : (a) Exact figure: 2 Marks
(b) Correct answer: 2 Marks

(a)

(b)

Free Symmetry Subjective Test 02 Practice Test - 7th grade

Question 1

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Question 2

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Question 3

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Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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