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Order of rotational symmetry of an equilateral triangle about the centroid of the triangle is 3.

Answer: Option B. -> False
:
B
Letters H and O have both line symmetry and rotational symmetry. Z has only rotational symmetry.

Answer: Option B. -> Arjun is right and Shubh is wrong
:
B
If a figure can be folded along any line such that one half superimposes or aligns exactly with the other, it is known as symmetric figure.
For example: If you take a square and fold it across the line shown, part 1 exactly overlaps part 2. So, 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, parallelogram is not symmetric.


Hence, Arjun is right and Shubh is wrong.

:
As it turns out, any figure which has point symmetry exhibits rotational symmetry around that point of symmetry. So, letters which have point symmetry will have rotational symmetry for sure. So, the letters that will fall under this category are:
H, I, N, O, S, X, Z
But we can’t be sure that these are the only letterswhich have rotational symmetry. A letter with rotational symmetry may not have point symmetry. Fortunately, there are no alphabets like that. So, 7 is the answer.

Answer: Option B. -> n−1
:
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.

Answer: Option B. -> False
:
B
Diagonal of a rectangle divides the rectangle into two triangles that are congruent, but folding along the line ABdoes not make the two triangles coincide with each other.
Hence AB is not a line of symmetry.

:
Each part: 1 Mark
(a)If a fan has rotational symmetry of order 4, thismeans 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.

:
Statement: 1 Marks​​​​​​
Reason: 1 Mark
The statement is not correct because $\frac{360}{17}$is not a naturalnumber, a figure can not have an angle of rotation as ${17}^{\circ }$.

:
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.

Answer: Option B. -> rotational symmetry
:
B
The letter 'S' whenrotated by an angle of ${180}^{\circ }$will look exactly the same as before.
Thus, it has rotational symmetry of order 2.
The letter S does not exhibit line symmetry.