Draw the line (or lines) of symmetry, if any, of the following shapes and count their number:
Answer
(i) The given shape is an ellipse. It can be folded into two coincident parts about its longer axis and about its shorter axis.
Hence, the given shape has 2 lines of symmetry.
(ii) The given shape is made up of two identical circles placed above and below a rectangular bar. It can be folded into two coincident parts about the vertical line through the centres of the two circles and about the horizontal line through the centre of the bar.
Hence, the given shape has 2 lines of symmetry.
(iii) The given shape is made up of three identical bars joined to one another. There is no line about which the figure can be folded so that its two parts coincide.
Hence, the given shape has no line of symmetry.
For each of the given shapes in question 1, find the order of the rotational symmetry (if any).
Answer
We know that,
If A° (≤ 180°) is the smallest angle through which a figure can be rotated about a fixed point and still looks the same as in its starting position, then the order of its rotational symmetry = .
(i) On rotating the given shape through 180° about the point of intersection of its two axes, it looks exactly the same as in its starting position.
Order of rotational symmetry = .
Hence, the given shape has rotational symmetry of order 2.
(ii) On rotating the given shape through 180° about the centre of the bar, it looks exactly the same as in its starting position.
Order of rotational symmetry = .
Hence, the given shape has rotational symmetry of order 2.
(iii) On rotating the given shape through 120° about its centre, it looks exactly the same as in its starting position.
Order of rotational symmetry = .
Hence, the given shape has rotational symmetry of order 3.
Write the letters of the word 'NEW ALGEBRA' which have no line of symmetry.
Answer
The word 'NEW ALGEBRA' is made up of the letters N, E, W, A, L, G, E, B, R and A.
The letters E and B each have one horizontal line of symmetry.
The letters W and A each have one vertical line of symmetry.
The letters N, L, G and R cannot be divided into two coincident parts by any line, so they have no line of symmetry.
Hence, the letters N, L, G and R of the word 'NEW ALGEBRA' have no line of symmetry.