5. Answer figures are:
Yes, there is more than one way.
Yes, this figure will be symmetric about both the diagonals.
8. (a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y
(b) Horizontal mirror – B, C, D, E, H, I, O and X
(c) Both horizontal and vertical mirror – H, I, O and X
9. The three examples are:
(ii) Scalene triangle
10. (a) The line of symmetry of an isosceles triangles is median or attitude.
(b) The line of symmetry of a circle is diameter.
11. Rotational symmetry of order more than 1 are (a), (b), (d), (e) and (f) because in these figure, a completer turn, more than 1 number of times, an object looks exactly the same. 12. Sol.
13. Circle and Square. 14. (i) An equilateral triangle has both line and rotational symmetries of order more than 1.
(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.
(iii) It is not possible because order of rotational symmetry is more than 1 of a figure, most acertain the line of symmetry.
(iv) A trapezium which has equal non-parallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
15. Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle. 16. Sol.
17. Square has both line and rotational symmetry of order more than 1.
18. Other angles will be 120°, 180°, 240°, 300°, 360°.
For 60° rotation: It will rotate six times.
For 120° rotation: It will rotate three times:
For 180° rotation: It will rotate two times.
For 360° rotation: It will rotate one time.
19. (i) If the angle of rotation is 45°, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle or rotational is 17°, then symmetry of order is not possible because 360° is not complete divided by 17°.