Important Questions: Symmetry - Free MCQ Test with solutions for

Recall definition of line symmetry. 

All of the letters have horizontal line of symmetry since it cut them in equal parts if we draw a line in the middle of each of the letters.

Line of symmetry: It is an imaginary line that when passes through any shape or letter, divides it into two equal halves or duplicates or we can say that when a shape or a letter is folded along the line of symmetry, the figure overlaps each other.

The letters F, G, J, L, N, P, Q, R, S and Z have no line of symmetry as the letters cannot be divided into two or more equal halves such that they overlap each other.

The alphabet 'O' has the most lines of symmetry because it is a circle, which has an infinite number of lines of symmetry. Any diameter can serve as a line of symmetry.

• The letter 'I' has only one vertical line of symmetry.
• Letters 'P' and 'F' have no lines of symmetry.

A scalene triangle, where all sides are different lengths and none of the angles are equal, lacks any line of symmetry because no reflection will map the triangle onto itself.

In contrast:

• Equilateral triangles have all sides equal and possess at least three lines of symmetry.
• Isosceles triangles have at least two equal sides and at least one line of symmetry.

Since horizontal mirror is mirror along with the x-axis , so B will be seen as B

Figure 1 has, in total, 4 lines of Symmetry
Figure 2 has 2 lines of symmetry 
So both figure 1 and 2 has minimum 2 lines of symmetry

Rotational symmetry of order n means the figure looks the same after a rotation of 360° ÷ n, and more than once in a full 360° turn. If it only matches after a full 360°, then its order is 1.

(a) Circle with two perpendicular diameters
When rotated by 90°, 180°, 270°, or 360°, it looks the same. So, it has rotational symmetry of order 4.

(b) Equilateral triangle
When rotated by 120°, 240°, or 360°, it looks the same. So, it has rotational symmetry of order 3.

(c) Four-leaf figure (like a pinwheel)
When rotated by 90°, 180°, 270°, or 360°, it looks the same. So, it has rotational symmetry of order 4.

(d) All of these
Since each of the given figures (a, b, c) has rotational symmetry of order greater than 1, the correct answer is d) All of these.

Final Answer (with explanation for exam): All three figures shown have rotational symmetry of order more than 1. The circle with diameter has order 4, the equilateral triangle has order 3, and the four-leaf figure has order 4. Hence, the correct option is d) All of these.

Line symmetry is also known as reflection symmetry.Because a mirror line resembles the line of symmetry, where one half is the mirror image of the other half.

The second figure has only the vertical line of symmetry. So it has only 1 line of symmetry.

There are only two possibilities i.e., diagonal lines of symmetry. So there are two lines of symmetry.

The figure formed is a rhombus.

A diameter divides the circle into 2 equal parts. So, it can be considered as a line of symmetry.

Since XY=XZ and XM⊥YZ,

∠YXM=∠ZXM. So, the triangle is symmetrical about XM as it bisects the apex angle.

The letter "Z" does have 2-fold rotational symmetry under certain conditions:

• Z has symmetry when rotated by 180° (half-turn) about its center. When you rotate the letter "Z" by 180°, it still looks the same (it coincides with its original position).
• Therefore, the order of rotational symmetry for Z is 2, because it matches itself when rotated by 0° and 180°.

The correct answer is indeed C: 2 because the letter "Z" has 2-fold rotational symmetry.

Quadrilaterals with symmetries of order more than 3 include:

• Square: A square has both line and rotational symmetry of order 4. It can be rotated by 90, 180, or 270 degrees, and it has 4 lines of symmetry.
• Kite: A kite has one line of symmetry but does not have rotational symmetry of order greater than 3.
• Rectangle: A rectangle has 2 lines of symmetry and rotational symmetry of order 2, which does not meet the criteria.
• Triangle: A triangle generally has fewer than 3 lines of symmetry unless it is an equilateral triangle, which still does not meet the criteria.

Among the listed quadrilaterals, only the square possesses both line and rotational symmetries of order greater than 3.

Rotational symmetry in capital letters describes a property in which the letter looks the same after being rotated. Capital letters that have rotational symmetry are: Z, S, H, N and O.
The letters Z, S, H and N, when rotated 180 degrees clockwise or counterclockwise, will look the same after rotation completion. This is called rotational symmetry on the order of two, because there were two 90 degree rotations. The letter O has rotational symmetry on the order of one, because after being rotated by 90 degrees, it still looks the same.

A square has a rotational symmetry of order 4. This means that it can be rotated about its centre four times during a full 360-degree rotation, and it will look the same at each of these rotations.

• The total angle of rotation for one complete turn is 360 degrees.

To find the angle of rotation for each position, divide 360 degrees by the order of symmetry, which is 4:

• Angle of rotation = 360 degrees / 4 = 90 degrees.

Hence, the angle of rotation for a square is 90 degrees.