GSEB Class 7 Maths Solutions Chapter 14 Symmetry Exercise 14.2

Question 1. Which of the following figures have rotational symmetry of order more than 1:
Answer: The figures (a), (b), (d), (e) and (f) possess rotational balance with an order greater than 1.
In simple words: This question asks us to identify the pictures that can be turned less than a full circle and still look exactly the same. We need to find the ones that have more than one way to look identical after rotating.

Exam Tip: To determine rotational symmetry, mentally rotate the figure around its center. Count how many times it looks identical before completing a full \( 360^\circ \) rotation. If it looks the same more than once (not counting the starting position), its order is greater than 1.

Question 2. Give the order of rotational symmetry for each figure:
Answer:
(a) Let us mark a point P as shown in the figure (i). It needs two rotations, each through \( 180^\circ \) about the center point (X) to return to its original position.
\( \implies \) It possesses a rotational symmetry of order 2.
(b) Mark a point P as shown in figure (i). It needs two rotations, each through an angle of \( 180^\circ \), about the marked point (X) to return to its starting position.
\( \implies \) So, it has a rotational symmetry of order 2.
(c) Mark a point P as shown in figure (i). It needs three rotations, each through an angle of \( 120^\circ \), about the marked point (X) to return to its original position.
\( \implies \) So, it has a rotational symmetry of order 3.
(d) Mark a point P as shown in Fig. (i). It needs four rotations, each through an angle of \( 90^\circ \), about the marked point (X) to return to its original position.
\( \implies \) So, it has a rotational symmetry of order 4.
(e) The figure needs four rotations each of \( 90^\circ \), about the marked point (X) to return to its initial position.
\( \implies \) It possesses a rotational symmetry of order 4.
(f) The figure is a regular pentagon. It needs five rotations, each through an angle of \( 72^\circ \), about the marked point to return to its original position.
\( \implies \) It possesses rotational symmetry of order 5.
(g) The given figure needs six rotations, each through an angle of \( 60^\circ \), about the marked point (X) to return to its original position.
\( \implies \) So, it has a rotational symmetry of order 6.
(h) The given figure needs three rotations, each through an angle of \( 120^\circ \), about the marked point (X), to return to its initial position.
\( \implies \) Its has a rotational symmetry of order 3.
In simple words: For each shape, rotate it around its center. Count how many times it looks exactly the same before it completes a full \( 360^\circ \) turn. This count is the "order of rotational symmetry". A higher order means it looks symmetrical more often when you spin it.

Exam Tip: To find the order of rotational symmetry, divide \( 360^\circ \) by the smallest angle of rotation that makes the figure look identical. For regular polygons, the order of symmetry is equal to the number of sides. Always clearly state the number of rotations and the angle for each part of the answer.