Page 266 - Ganit Kaushal

Assertion Reason Type Questions
A statement of assertion (A) is followed by a statement of reason (R). Choose the correct option out of the
choices given below for each question:
(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
1. Assertion (A): A diagonal of a square is also a line of symmetry.
Reason (R): When a figure is folded about a line of symmetry, the two halves perfectly overlap.
2. Assertion (A): A diagonal of a rectangle is also a line of symmetry.
Reason (R): When a figure is folded about a line of symmetry, the two halves perfectly overlap.
3. Assertion (A): A circle has an infinite number of lines of symmetry.
Reason (R): Every diameter of a circle is a line of symmetry, and there are infinitely many diameters
of a circle.
4. Assertion (A): A regular hexagon has six lines of symmetry.
Reason (R): A regular polygon has as many lines of symmetry as the number of sides.
5. Assertion (A): The letter ‘M’ has a vertical line of symmetry.

Reason (R): Symmetry in an object means one half of the figure is a mirror image of the other.
6. Assertion (A): The given figure has rotational symmetry of order 2.
Reason (R): A figure can be rotated by 180° to fit into itself.
7. Assertion (A): A rhombus has 2 lines of symmetry.
Reason (R): The lines of symmetry of a shape always pass through its vertices.
8. Assertion (A): The least angle of symmetry is a divisor of all angles of symmetry.
Reason (R): A circle has an infinite number of lines of symmetry.

Summary of the Chapter

• Symmetry means that one shape becomes exactly like another when it is turned at some angle, flipped
or slid (horizontally, vertically or at some inclination).
• The simplest type of symmetry is reflection (or mirror) symmetry. An object is symmetrical when half
of it is a mirror image of the other half. It may be divided by one or more lines of symmetry.
• A line of symmetry divides a shape into two equal and identical parts.
• Sometimes a figure looks exactly the same when it is rotated by an angle about a fixed point. Such an
angle is called an angle of symmetry of the figure. A figure that has an angle of symmetry strictly between
0° and 360°, is said to have rotational symmetry. The point of the figure about which the rotation occurs
is called the centre of rotation.
• Reflection and rotational symmetry can be found in geometric figures, in some English alphabets, digits
and in nature.
• A symmetrical object may have more than one line and angle of symmetry.
• If the number of lines of symmetry is 0, then the shape does not have any linear symmetry.
• If the number of angles of symmetry is 1, then the shape does not have any rotational symmetry.

264 Mathematics-6