# Free Symmetry Subjective Test 01 Practice Test - 7th grade

How many lines of symmetry does an equilateral triangle have?  [1 MARK]

#### SOLUTION

Solution :

The line of symmetry is a line which divides the given diagram into two equal mirror images. So, here the number of lines are 3. (a) What are the two names of the line of symmetry of an isosceles triangle?
(b)
Which capital letters of English alphabets have no line of symmetry?  [2 MARKS]

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Solution : Each part: 1 Mark

(a) The line of symmetry of an isosceles triangle is also known as median or altitude.
(b)
Capital letters of English alphabet having no line of symmetry are F, G, J, L, N, P, Q, R, S and Z.

(a) Which of the following letters have horizontal symmetry?
E, G, C, B, O, W

(b) Find the number of lines of symmetry for the given figure. [2 MARKS] #### SOLUTION

Solution : Each part: 1 Mark

(a) The following letters have horizontal symmetry:
B, C, E and O

(b) There are four lines of symmetry for the given figure. (a) If a fan has a rotational symmetry of order 4, how many blades are there in the fan?
(b) Name the quadrilateral which has both line and rotational symmetry of order more than 1.  [2 MARKS]

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Solution :

Each part: 1 Mark

(a) If a fan has rotational symmetry of order 4, this means that the fan looks exactly as it was before the rotation at four instances. This can only happen when it has four blades.

(b) Square has both line and rotational symmetry of order more than 1.

(a) Edward has a shining star as shown below. What is the total number of lines of symmetry in this star? (b) How many lines of symmetry does a regular pentagon have?  [2 MARKS]

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Solution :

Each part: 1 Mark

(a) In order to identify the total number of lines of symmetry, we first have to identify the line through which we can fold the figure in such a way that two parts can overlap each other. Hence we find that this figure has five lines of symmetry. (b) A
regular pentagon has 5 lines of symmetry. How many lines of symmetry do the following figures have?  [3 MARKS]

(i) (ii) (iii) #### SOLUTION

Solution :

Figures: 1 Mark each

(i) 1 line of symmetry (ii) 1 line of symmetry​​​​​​​ (iii) 1 line of symmetry If a random diagram can be cut into fourteen equal parts, how many lines of symmetry does it have? Draw such a diagram. [3 MARKS]

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Solution :

No. of lines of symmetry: 1 Marks
Diagram: 2 Marks

Any line which divides a diagram into two equal halves is called a line of symmetry. This line of symmetry divides the figure into two identical halves. If a random diagram has 7 such lines, it will have 7 lines of symmetry.

The most basic figure that would have 7 lines of symmetry would be a regular heptagon with all 7 sides equal. Such a figure will have 7 lines of symmetry. (i) How many of the given alphabets have rotational symmetry:
Z, H, E, N, C

(ii) Give the order of the rotational symmetry of each figure.  [3 MARKS]

#### SOLUTION

Solution :

(i) Z, H, N have rotational symmetry.
If the given alphabets are rotated about a line passing through their centres, it resembles the same alphabet.

(ii)
(a)

 Original Figure Rotational figures Order of rotational symmetry  2

(b)
 Original Figure Rotational figure Order of rotational symmetry  2

(a) Investigate and find out the order of rotational symmetry of the below figure. (b) How many lines of symmetry does a parallelogram have?
[3 MARKS]

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Solution :

Diagram: 1 Mark

(a) For every 90 degrees of rotation, the figure looks the same. Therefore the figure has an order of rotational symmetry of 4.

(b) A parallelogram has no line of symmetry. Number of lines = 0

Complete the following diagrams by drawing the mirror images.  [4 MARKS]

(i) (ii) (iii) (iv) #### SOLUTION

Solution :

Completed Figures: 1 Mark each

(i) (ii) (iii) (iv) (a) Given that the diagram has 5 lines of symmetry. Draw all the lines of symmetry and then divide the figure into 10 parts. Given here is a part of the diagram. Complete the diagram. (b) How many lines of symmetry do a polygon with its adjacent sides equal and perpendicular have?
[4 MARKS]

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Solution :

Each option: 2 Marks

(a) The asked diagram is a pentagon. (b)  A polygon with adjacent sides equal and perpendicular is a square. A square has 4 lines of symmetry. (a) After rotating through an angle of 120 degrees through its centre of symmetry the figure looks exactly the same as its original. At what other angles will it happen for the figure? Describe with an example.

(b) What is the order of rotational symmetry?

(c) What is the order of rotational symmetry of a semi-circle?
[4 MARKS]

#### SOLUTION

Solution :

Example along with diagram: 1 Mark
(b) Definition: 1 Mark

(a) If it happens for 120, it will also happen for multiples of 120, such as 240 and 360.

The example is an equilateral triangle. (b) The number of position in which the object looks exactly the same is called the order of rotational symmetry.

(c) The order of rotational symmetry of a semicircle is 1.

A figure has no line of symmetry but a rotational symmetry of 2. Draw and name the respective figure? Find its area given that its side length is 5m and base length is 6m and height is 4m.  [4 MARKS]

#### SOLUTION

Solution :

Correct name: 1 Mark
Diagram: 1 Mark
Formula for area: 1 Mark
Result: 1 Mark

A general parallelogram is a geometric figure which does not have any line of symmetry. It, however, has an order of rotational symmetry of 2 as we get the same figure when it's rotated by 180 or 360.

For example, if we rotate the following figure by 180, we will still get an identical figure, hence it has an order of rotational symmetry as 2. For a parallelogram, the area is given by  Base x Height
According to question, Base = 6m and Height = 4m

Area = 6×4 = 24m2

Mention the order of rotational symmetry in the following figures:  [4 MARKS] #### SOLUTION

Solution : Figures with order of symmetry 4: 1 Mark
Figures with order of symmetry 3: 1 Mark
Figures with order of symmetry 2: 1 Mark
Figures with order of symmetry 1: 1 Mark

Figures (a) and (f) will look the same if rotated by 90o, 180o, 270o or 360o. Hence, they have an order of 4.

Figures (b) and (e) will look the same if rotated by 120o, 240o or 360o. Their order of rotational symmetry will thus be 3.

If we rotate figure (d) by 180o or 360o, we will get the same figure. Hence, it has an order of 2.

But option (c) has an order of only 1 since the same figure can be obtained if the figure is rotated by 360o.

(i) What letters of the English alphabet have reflection symmetry about:
a) A Vertical mirror
b) A Horizontal mirror

(ii)  <Two friends arguing>

Suraj: If a figure can be folded along any line such that one half superimposes the other, it is known as a symmetric figure.

Ravi: If you can find a line in the figure which divides it into identical parts, then the figure is always symmetric.

Who is correct?
[4 MARKS]

#### SOLUTION

Solution : (i) Answer: 2 Marks

a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y Horizontal mirror - B, C, D, E, H, I, O and X (ii)  If a figure can be folded along any line such that one half superimposes or aligns exactly with the other, it is known as a symmetric figure. For e.g. If you take a square and fold it across the line shown, part 1 exactly overlaps on part 2. So, the square is a symmetric figure. On the other hand, in a parallelogram, the diagonal divides it into two congruent triangles (can be proven using SSS congruence condition), i.e. into two equal parts. But those parts don’t superimpose each other when folded across diagonal (as shown in the figure). So, the parallelogram is not symmetric.  Hence, Suraj is right and Ravi is wrong.