GSEB Class 7 Maths Solutions Chapter 14 સંમિતિ Exercise 14.2

Question 1. નીચે આપેલી કઈ આકૃતિમાં પરિભ્રમણીય સંમિતિનો ક્રમ 1 કરતાં વધુ છે?
(a)
(b)
(c)
(d)
(e)
(f)
Answer:
(a) This figure returns to its original position after rotating 4 times by an angle of 90 degrees. So, its order of rotational symmetry is 4.
(b) This figure returns to its initial position after rotating 3 times by an angle of 120 degrees. So, its order of rotational symmetry is 3.
(c) This figure has an order of rotational symmetry of 1.
(d) This figure returns to its starting position after rotating 2 times by an angle of 180 degrees. So, its order of rotational symmetry is 2.
(e) This figure returns to its first position after rotating 3 times by an angle of 120 degrees. So, its order of rotational symmetry is 3.
(f) This figure returns to its base position after rotating 4 times by an angle of 90 degrees. So, its order of rotational symmetry is 4.
Therefore, from the figures given above, figures (a), (b), (d), (e), and (f) have a rotational symmetry order greater than 1.
In simple words: You need to find which shapes can be turned around more than one time to look exactly the same again. This means their "turn symmetry" number is bigger than 1.

Exam Tip: To find the order of rotational symmetry, identify the smallest angle by which a figure must be rotated to look identical, then divide 360 degrees by this angle.

Question 2. દરેક આકૃતિ માટે પરિભ્રમણીય સંમિતિનો ક્રમ જણાવો.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Answer:
(a) This figure comes back to its starting look after two rotations of 180 degrees around point X. Hence, its order of rotational symmetry is 2.
(b) This figure returns to its initial appearance after two rotations of 180 degrees around point X. Hence, its order of rotational symmetry is 2.
(c) This figure goes back to its original form after three rotations of 120 degrees around point X. Hence, its order of rotational symmetry is 3.
(d) This figure achieves its initial position after four rotations of 90 degrees around point X. Hence, its order of rotational symmetry is 4.
(e) This figure gets back to its starting state after four rotations of 90 degrees around point X. Hence, its order of rotational symmetry is 4.
(f) This figure reaches its initial setup after five rotations of 72 degrees around point X. Hence, its order of rotational symmetry is 5.
(g) This figure comes to its first appearance after six rotations of 60 degrees around point X. Hence, its order of rotational symmetry is 6.
(h) This figure goes back to its original look after three rotations of 120 degrees around point X. Hence, its order of rotational symmetry is 3.
In simple words: For each picture, tell us the total number of times it looks exactly the same when you turn it all the way around in a full circle.

Exam Tip: To check your answer, multiply the smallest angle of rotation by the order of rotational symmetry; the result should always be 360 degrees.