# Free Symmetry Subjective Test 02 Practice Test - 7th grade

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

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Solution :

Two lines of symmetry are possible for a rectangle. Which of the following letters have vertical symmetry? Explain with reason.  [2 MARKS]
A, C, E, H, S, V, Z

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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.

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

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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.

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

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Solution :

Statement: 1 Marks​​​​​​
Reason: 1 Mark

The statement is not correct because 36017 is not a natural number, a figure can not have an angle of rotation as 17.

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

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Solution :

Correct Answer: 1 Mark
Diagram: 1 Mark

A parallelogram has 0 lines of symmetry. 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.

Given that the perimeter of a polygon is 92m and its area is 529m2. Its adjacent sides are equal and perpendicular. Find the number of lines of symmetry.
[3 MARKS]

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Solution :

Process: 2 Marks
Result: 1 Mark

The given polygon is square.

Perimeter 4a = 92

a = 23 m

Area = a2 = 529 m2

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

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 Find the number of lines of symmetry for the following figures.
(a) (b) [3 MARKS]

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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 (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]

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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 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, 180 and 270. It’s only 3, not 4.

(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]

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Solution :

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

(a) The answer is 2. The given diagram when rotated by 180o and 360o gives the same figure. Due to different colours of the two diagonals, the figure won't look the same if it's rotated by 90o or 270o. 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 rotation.

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

This is because the last rotation, i.e. 360 is not counted as angle of rotation.

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

(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]

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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 m2

(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.

(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]

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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. (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]

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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

(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]

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

(a) (b) 