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Cycle wheel is having clockwise and anti clock wise both rotations.

If any object is divided in two halves by a point or dotted line and each halves match each other exactly then it is called symmetry.

(a) In a vertical mirror english alphabets reflection alphabets are following:

A, H, I, M, O, T, U, V, W, X, Y

(b) in horizontal direction following english alphabets are symmetrical

B, C, D, E,H, 1,0 and X

(c) Following english alphabets are having vertical and horizontal symmetry H, I, O and X.

(a) Yes

(b) Yes

(c) No

(d) Yes

(e) Yes

(f) Yes

A, O and T having same mirror image as the object or letters.

(a) Vertical lines of symmetry (like A)

A, H, I, M, 0, T, U, V, W, X, Y

(b) Horizontal lines of symmetry (like B)

B, C, D, E, H, I, K, Q, X

(c) No lines of symmetry (like Q)

F, G, J, L, N, P, Q, R, S, Z

Paper, Sheet, Glass, Cd, Bucket.

i) p

ii) two

iii) two

iv) two

v) Translation

Yes, Horizontal.

Wall clock, dining table top, bucket, photo frame etc.

Yes, human faces symmetrical.

No, not equal.

In the word ‘FIGURE’ the symmetrical letters are I, U and E.

Yes, the two parts of both the figures fall on each other on folding along the line l.

(1) F G J

(2) Scalene triangle

(3) Parallelogram

Have no line of symmetry.

a. a vertical mirror

A H I M O T U V W X Y

These letter have vertical symmetry

b. a horizontal mirror

B C D E H I O X

These letter have horizontal symmetry.

c. both horizontal and vertical mirrors

H I O X

These have both horizontal and vertical symmetry

The image of a point lying on a line l with respect to the line of symmetry l lies on line l.

If a line segment of length 5cm is reflected in a line of symmetry (mirror), then its reflection (image) is a line segment of length 5cm.

(B) (ii)

A figure is said to have line symmetry, if by folding the figure along a line, the left and right parts of it coincide exactly. The line is called the line (or axis) of symmetry of the figure.

Drawn dashed line are line of symmetry for following figures 

(i), 

(ii), 

(iii), 

(v), 

(vi) 

Dashed line is not a line of symmetry for figure 

(iv).

4

The letters are H, I, O and X having both horizontal and vertical line of symmetry.

No

A 30° – 60° – 90° set-square has no line/lines of symmetry.

Other angles will be as follows : 120°, 180°, 240°, 300°, 360°.

In the three rotation of equilateral triangle every rotational angle will be 120°.

(i) Rectangle

(ii) Parallelogram

Angle between successive axes of

Symmetry = 45° = \(\frac {360°}{2n}\)

This is true for all regular polygons.

(i) Circle

(ii) Square

The above figure (i), (ii), (iii), (iv), (v) have rational symmetry of order more than 1.

The above figure (i), (ii), (iii), (iv), (v) have rational symmetry of order more than one.

Circle, wheel, square etc.

i) Order of rotational symmetry for an equilateral triangle = 120° 

ii) 3 lines. 

iii) 120°

The circle can be rotated through any angle to get rotational symmetry.

(i) Order 2 

(ii) Order 4 

(iii) Order 3 

(iv) Order 4 

(v) Order 4 

(vi) Order 5 

(vii) Order 6 

(viii) Order 3

(i) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 4.

(ii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 3.

(iii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 3.

(iv) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 4.

(v) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 2.

(vi) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 4.

(vii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 5.

(viii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 6.

(ix) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360°

Therefore the given figure has its rotational symmetry as 3.

(i) The letter of the English alphabet which has no line of symmetry is Z.

(ii) The letter of the English alphabet which has rotational symmetry of order 2 is N.

(a) Triangle, yes

(b) Rectangle, Yes

(c) Parallelogram, no. 

Yes, infinite since every diameter of a circle is an axis at symmetry for the circle and there are an infinite number of diameter in a circle.

(i) False

(ii) True

(iii) False

Correct option is D) All the above

Correct option is A) 4

Correct option is D) All the above

Correct option is D) Infinite