Mathematics
Assertion: The number of lines of symmetry of a regular polygon is equal to its number of vertices.
Reason: A figure that possesses point symmetry always has line symmetry.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.
Symmetry
2 Likes
Answer
Assertion (A) is true but Reason (R) is false.
Explanation
For any regular polygon (like an equilateral triangle, square, or regular pentagon), the number of lines of symmetry is equal to the number of sides, which is also equal to the number of vertices.
For example, a square has 4 vertices and 4 lines of symmetry.
So, Assertion is true.
Point symmetry is rotational symmetry of order 2 (looking the same upside down). However, a figure can have point symmetry without having any lines of symmetry.
A classic example is the letter 'S' or a parallelogram. You can rotate them 180° to match, but you cannot fold them to get mirror images.
So, Reason is false.
Hence, option 3 is the correct option.
Answered By
3 Likes
Related Questions
Which of the following letters of English alphabet has a rotational symmetry?
- C
- K
- N
- T
Fill in the blanks :
(i) A circle has …………… lines of symmetry.
(ii) The letter S does not possess …………… symmetry.
(iii) A semi-circle is symmetrical about the …………… of its diameter.
(iv) The letter H has …………… line(s) of symmetry.
(v) A quadrilateral having 4 lines of symmetry as well as rotational symmetry of order 4 is …………… .
Write true (T) or false (F) :
(i) A kite possesses a linear symmetry but no rotational symmetry.
(ii) The order of rotational symmetry of a regular hexagon is 6.
(iii) A parallelogram does not have any line of symmetry.
(iv) A square has a point symmetry but rhombus does not.
(v) The letter N does not possess a rotational symmetry.
Assertion: Order of rotational symmetry for the given figure is 4.
Reason: A figure is said to possess rotational symmetry if it fits on itself more than once while being rotated through 360°.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.