NCERT Solutions Ganita Prakash Chapter 9 Figure it Out

Q1.

Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?

Answer

Yes — three of the four figures can be folded into mirror halves; the pinwheel and the cloud cannot.

Figure	Lines of symmetry	Where they are
Flower (6 petals)	6	one along each petal and one between every two petals
Rangoli	4	vertical, horizontal and the two slanting lines through the centre
Butterfly	1	the vertical line along its body
Pinwheel	0	every blade leans the same way, so no fold works
Cloud	0	nothing in it repeats at all

Note the difference: the pinwheel has no line of symmetry but it does look the same after a 60° turn. The cloud has neither — it is not symmetrical in any way.

Q2.

For each of the following figures, identify the line(s) of symmetry if it exists.

Answer

Three of the five figures have exactly one line of symmetry; two have none. The dashed red lines below are the lines of symmetry.

The five figures of page 219 with their lines of symmetry drawn as dashed lines.

(i) The arrow-shaped figure — 1 line of symmetry: the line through the V-shaped notch and the opposite corner. Folding along it makes the upper point fall on the lower point.
(ii) The kite — 1 line of symmetry: the vertical line joining the top corner to the bottom corner. (Its other diagonal is not a line of symmetry, because the two parts are of different sizes.)
(iii) The four-sided figure with two vertical sides of different lengths — no line of symmetry. No fold makes the short side fall on the long side.
(iv) The L-shape — 1 line of symmetry: the slanting diagonal from the outer corner to the inside corner. Both arms have the same length and the same thickness, so they swap over exactly.
(v) The thin triangle — no line of symmetry. All its three sides are of different lengths (a scalene triangle).

Check it yourself: trace each figure on paper, cut it out and try folding it in every way you can. A fold works only when the two parts cover each other completely — no part sticking out.

NCERT Solutions Ganita Prakash Chapter 9 Figure it Out — Line of Symmetry