Worksheet Solutions: Symmetry - 1

Multiple Choice Questions (MCQs)

Q1: How many angles of symmetry does a square have?
(a) 2
(b) 4
(c) 6
(d) 8
Ans: (b) 4
Solution: A square has rotational symmetry at angles of 90°, 180°, 270°, and 360°.

Q2: When a figure is rotated by 180° and it looks exactly the same, the figure has _______ symmetry.
(a) Reflection
(b) Rotational
(c) Translational
(d) No
Ans: (b) Rotational
Solution: A figure with rotational symmetry looks the same after a 180° rotation.

Q3: Which of the following figures has both reflection symmetry and rotational symmetry?
(a) Rhombus
(b) Regular pentagon
(c) Circle
(d) Isosceles triangle
Ans: (c) Circle
Solution: A circle has infinite lines of symmetry and rotational symmetry.

Q4: How many lines of symmetry and angles of symmetry does Ashoka Chakra have?
(a) 12
(b) 24
(c) 48
(d) 10
Ans: (b) 24

Solution: The Ashoka Chakra has 24 equally spaced spokes.
Therefore:

• It has 24 lines of symmetry.
• It also has rotational symmetry of order 24 (it matches itself 24 times in a full rotation).

Hence, the required number is 24.

Line of Symmetry

Draw Line of Symmetry for the following shapes

(a)

(b)

(c)

Ans:

(a)

(b)

(c)

Fill in the Blanks

Q1: A line that divides a figure into two identical halves is called a _______ of symmetry.
Ans: Line
Solution: A line of symmetry is a line that divides a figure into two identical parts, where one half is the mirror image of the other.

Q2: The shape of a _______ remains the same when rotated by any angle.
Ans: Circle
Solution: A circle has infinite lines of symmetry and remains unchanged no matter the angle of rotation.

Q3: A square has _______ lines of symmetry.
Ans: 4
Solution: A square can be divided into two identical halves along four lines: two diagonals, one vertical, and one horizontal.Q4: A figure with no line of symmetry is called _______.
Ans: Asymmetrical
Solution: An asymmetrical figure cannot be divided into two identical halves.

Q5: The _______ is the point around which a figure is rotated in rotational symmetry.
Ans: Centre of rotation
Solution: The center of rotation is the fixed point around which a figure rotates to show symmetry.

True/False

Q1: Every shape with a line of symmetry must also have rotational symmetry.
Ans: False
Solution: Some shapes may have a line of symmetry but lack rotational symmetry, and vice versa.

Q2: A rectangle has two lines of symmetry.

Ans: True
Solution: A rectangle has two lines of symmetry: one vertical and one horizontal.

Q3: The number of angles of symmetry in a hexagon is four.

Ans: False
Solution: A regular hexagon has six angles of symmetry, corresponding to rotations of 60°, 120°, 180°, 240°, 300°, and 360°.

Q4: A circle has an infinite number of lines of symmetry.

Ans: True
Solution: Any circle's diameter can be a line of symmetry, so there are infinite such lines.

Q5: The smallest angle of symmetry in the Ashoka chakra is 30°.

Ans: False
Solution: There are 24 lines in Ashoka chakra. Therefore, Smallest angle of symmetry = 360° ÷ 24 = 15°.