Question 1 - Figure it out - Page 238, 239 - Chapter 9 Class 6 - Symmetry (Ganita Prakash)

Transcript

Question 1 Colour the sectors of the circle below so that the figure has i) 3 angles of symmetry, ii) 4 angles of symmetry, iii) what are the possible numbers of angles of symmetry you can obtain by colouring the sectors in different ways?The circle has 12 sectors. This figure has 12 angles of symmetry (also called the "order" of symmetry) So, Number of sectors = Number of angles 3 angles of symmetry 3 angles of symmetry means the figure must look identical 3 times during a full 〖𝟑𝟔𝟎〗^∘ rotation. The angles would be 〖𝟏𝟐𝟎〗^∘,〖𝟐𝟒𝟎〗^∘, and 〖𝟑𝟔𝟎〗^∘. The Math: To make a 12 -sector circle repeat 3 times, you must divide the 12 sectors into 3 identical groups. 12" sectors "÷3" groups "=𝟒" sectors per group " The Pattern: This means your coloring pattern must repeat every 4 sectors. The Solution: You should color 1 sector, then skip 3 sectors, then color 1 sector, then skip 3 sectors, and finally color the 1 remaining sector. This creates a balanced, 3-pointed shape that looks the same after every 120^∘ turn. Let’s do this Checking Rotational Symmetry 4 angles of symmetry 4 angles of symmetry means the figure must look identical 4 times during a full 〖𝟑𝟔𝟎〗^∘ rotation. The angles would be 90° , 180°, 270° and 360° The Math: To make a 12 -sector circle repeat 4 times, you must divide the 12 sectors into 4 identical groups. 12" sectors "÷4" groups "=𝟑" sectors per group " The Pattern: This means your coloring pattern must repeat every 3 sectors. The Solution: You should color 1 sector, then skip 2 sectors, then color 1 sector, then skip 2 sectors, and finally color the 1 remaining sector. This creates a balanced, 4-pointed shape that looks the same after every 90° turn. Let’s do this Checking Rotational Symmetry Checking Rotational Symmetry 270° + 90° = 360° 180° + 90° = 270° 90° + 90° = 180°