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MATHS 3 Marks Question

Symmetry. · Gujarat Board (GSEB) STD 6 (GSEB - English Medium). 9 questions.

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Question 13 Marks
How many lines of symmetry and angles of symmetry does Ashoka Chakra have?
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Answer
The Ashoka Chakra has 24 spokes spread equally.
24 spokes make 12 pairs.
Line through an opposite pair is a line of symmetry.
Hence, there are 12 lines of symmetry.
Smallest angle of symmetry = $ 360^{\circ} $ ÷ 2 = $ 30^{\circ} $.
Other angles of symmetry are its multiple up to 360.
Other angles are $ 60^{\circ} $, $ 120^{\circ} $, $ 150^{\circ} $, ………… , $ 360^{\circ} $. (12 angles in all).
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Question 23 Marks
How many lines of symmetry do the shapes in the first shape sequence in Chapter 1, Table 3, the Koch Snowflake sequence, have? What angle of symmetry?
Answer

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The triangular shape has 3 lines of symmetry and 3 angles of symmetry.
In six-pointed stars, lines of symmetry are 12 and the angle of symmetry is 6.
The lines of symmetry and angle of symmetry for the rest three figures are the same as six-pointed stars.
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Question 33 Marks
Can we have a figure with rotational symmetry whose smallest angle of symmetry is
(a) $45^{\circ}$?
(b) $17^{\circ}$?
Answer
(a) Since, the complete rotation is $360^{\circ}$. Then, if the given angle divides $360^{\circ}$, it can be an angle of symmetry.
Here, $\frac{360^{\circ}}{45^{\circ}}=8$, which is a whole number.
Therefore, $45^{\circ}$ can be the smallest angle of symmetry of a figure.
(b) Here, $\frac{360^{\circ}}{17^{\circ}}=21 \frac{3}{17}$, which is not a whole number. Therefore, $17^{\circ}$ cannot be the smallest angle of symmetry.
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Question 43 Marks
Color the sectors of the circle below so that the figure has
(a) 3 angles of sjjmmetry
(b) 4 angles of symmetry
(c) what are the possible numbers of angles of symmetry you can obtain by coloring the sectors in different ways?
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Answer
(a) Will look same after every rotation of 120°.
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(b) Will look same after every rotation of 90°.
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(c) Four ways are possible.
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Question 53 Marks
Find the angle of symmetry for the given figures about the point marked.
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Answer
(a) $90^{\circ}$
(b) $360^{\circ}$
(c) $180^{\circ}$
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Question 63 Marks
Draw the following.
A triangle with no line of symmetry
Is it possible to draw a triangle with exactly two lines of symmetry?
Answer

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A scalene triangle has no lines of symmetry.
No, it is not possible to draw a triangle with exactly two lines of symmetry.
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Question 73 Marks
How many lines of symmetry do these shapes have?
(i)
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(ii) A triangle with equal sides and equal angles.
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(iii) A hexagon with equal sides and equal sides.
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Answer
(i) A diamond has 4 lines of symmetry, and the figure next to it has 4 lines of symmetry.
(ii) An equilateral triangle has three lines of symmetry.
(iii) A regular hexagon has six lines of symmetry.
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Question 83 Marks
In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded. Identify the line along which the paper was folded.
Figure (d) was created by punching a single hole. How was the paper folded?
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3 Marks Question - MATHS STD 6 Questions - Vidyadip