GSEB Class 7 Maths Solutions Chapter 14 Symmetry InText Questions

Chapter 14 Symmetry InText Questions

Try These (Page 272)

Question 1. (i) Can you now tell the order of the rotational symmetry for an equilateral triangle? (Look at the following figures.)
(b) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by 120°?
Answer:
(i) An equilateral triangle shows exactly three points where it appears identical. Consequently, it has a rotational symmetry of order 3.
(b) When rotated about its center by 120 degrees, the triangle will appear precisely the same in just one position.
In simple words: An equilateral triangle can look the same in three ways when you spin it. If you turn it by 120 degrees, it will look exactly the same only once.

Exam Tip: Remember that the order of rotational symmetry indicates how many times a figure matches its original appearance during a full 360° rotation.

Question 2. Which of the following shapes have rotational symmetry about the marked point?
Answer: All the shapes displayed above, specifically (i), (ii), (iii), and (iv), possess rotational symmetry around the marked point (X).
In simple words: All the pictures shown can be turned around their center point and still look exactly the same.

Exam Tip: To test for rotational symmetry, mentally rotate the shape about the marked point and count how many times it aligns with its original form before completing a full circle.

Do This (Page 272-273)

Draw two identical parallelograms, one ABCD on a piece of paper and the other A' B' C' D' on a transparent sheet. Mark the points of intersection the parallelograms such that A' lies on A, B' lies on B and so on. O' then falls on O. Stick a pin into the shapes at the point O.

Now turn the transparent shape in the clockwise direction.

Question. (i) How many times do the shapes coincide in one full round?
(ii) What is the order of rotational symmetry?
Answer:
(i) If we turn the transparent shape anti-clockwise, we will notice two points where the shapes match up: first, when A' aligns with A, and second, when A' moves to C. This indicates that in a complete 360-degree rotation, the parallelogram has two positions where it appears identical.
(ii) The parallelogram therefore shows rotational symmetry of order 2.
In simple words: When you spin the parallelogram, it looks the same twice in a full circle. So, its rotational symmetry order is 2.

Exam Tip: The order of rotational symmetry is the number of times a figure looks the same during a 360-degree rotation. For a parallelogram, this happens twice.

Note: In this case the point where we have the pin is the centre of rotation. It is the meeting point of the diagonals.

Try These (Page 273)

Question 1. Give the order of the rotational symmetry of the given figures about the point marked.
Answer:
(i) The figure's rotational symmetry order is 4.
(ii) The figure's rotational symmetry order is 3.
(iii) The figure's rotational symmetry order is 4.
In simple words: The first picture and the third picture look the same 4 times when spun around. The second picture looks the same 3 times when spun around.

Exam Tip: Practice identifying common shapes (like squares, triangles, stars) and their corresponding rotational symmetry orders to quickly answer these types of questions.

Note: Every object always possesses rotational symmetry of order one, because it returns to the same position after a full 360-degree rotation, or a complete spin.

Do This (Page 275)

Question 1. Some of the English alphabets have fascinating symmetrical structures. Which capital letters have just one line of symmetry (like E)? Which capital letters have a rotational symmetry of order 2 (like I)? By attempting to think on such lines, you will be able to fill in the following table:
Answer:

Exam Tip: To determine line and rotational symmetry for letters, draw them clearly and try folding or rotating them mentally. Letters like 'H' and 'O' are common examples with multiple symmetries.