GSEB Class 6 Maths Solutions Chapter 13 Symmetry InText Questions

Try These (Page 262)

Question 1. You have two set-squares in your mathematical instruments box. Are they symmetrical?
Answer: The two set-squares you have are:The 30°-60°-90° set-square is not symmetrical. The 45°-45°-90° set-square is symmetrical.
In simple words: Out of the two types of set-squares in your geometry box, the one with angles 45°-45°-90° has symmetry, but the 30°-60°-90° one does not.

Exam Tip: To check for symmetry, try folding the shape along a line. If both halves match perfectly, the shape is symmetrical along that line.

Try These (Page 264)

Question 1. Form as many shapes as you can by combining two or more set-squares. Draw them on squared paper and note their lines of symmetry.
Answer: We can create several figures by joining two or more set-squares together. Here are some examples with their lines of symmetry:
(i) By joining two identical 30°-60°-90° set-squares, we get the following symmetrical figures:
(a) This figure shows a rectangle where \(l_1\) and \(l_2\) are its lines of symmetry.
(b) This figure shows a kite, and 'm' is its single line of symmetry.
(c) Here, the dotted line 'q' is the only line of symmetry.
(d) Here, the dotted line 'q' is the only line of symmetry.
(ii) By joining two identical 45°-45°-90° set-squares, we get the following symmetrical figures:
(a) Here, \(l_1\), \(l_2\), \(l_3\), \(l_4\) are all lines of symmetry.
(b) In the figure formed, there is only one line of symmetry which is shown by 'r'.
(iii) By joining three 45°-45°-90° identical set-squares, we can make an isosceles trapezium, as shown here. The line of symmetry is shown by the dotted line 'q'.
In simple words: We can create many shapes by joining set-squares. For each shape, we then find the lines along which it can be folded to match perfectly. Some shapes have many lines of symmetry, while others have only one.

Exam Tip: Always remember to look for all possible lines of symmetry, not just the obvious ones. A square, for example, has four lines of symmetry.

Try These (Page 270)

Question 1. If you are 100 cm in front of a mirror, where does your image appear to be? If you move towards the mirror, how does your image move?
Note: In the mirror reflection, there exists a lateral difference between the object and the image. The lateral difference means the left part of the object becomes the right part of the image and vice versa.
Answer: In a mirror, an image always appears at the same distance behind the mirror as the real object is positioned in front of it. Therefore, your image will show up 100 cm behind the mirror. If you start to move closer to the mirror, your image will also move closer, mirroring your movements.
In simple words: Your image will show up 100 cm behind the mirror. When you walk towards the mirror, your image also moves closer to it.

Exam Tip: Remember that mirror images are always laterally inverted, meaning left and right are swapped, but the distance from the mirror is preserved.