SA2 2015 16‐ ‐OPEN TEXT BASED ASSESSMENT

CLASS VII MATHS (THEME 2)‐

NATURE LOVES SYMMETRY

It seems nature loves symmetry , when you look around yourself there are numerous things which are symmetrical such as leaves , flowers, animals and to add even our bodies are symmetrical.

Fig 1 LEAF Fig 2 STAR FISH‐ ‐The spiders web is a beautiful example of symmetry. The idea of symmetry, it seems, were also appreciated by the early humans . It is clearly exhibited in their drawings. Given below are some of the drawings dated 5000BC

Fig 3 SPIDER’S WEB Fig 4 Fig 4 is an Example of the symmetry group : (a) the two headed winged lion (Tell Hallaf, about 5000 B.C.); (b) formation of motifs with the symmetry (cave paintings, La Pileta, Spain); (c) art of the pre dynastic period of Egypt; (d) motif from the Ionian amphora; (e) two headed Mayans snake; (f) primitive art of the American Indians

Harshika , a student of class VII, learnt that there are two types of symmetry namely Linear Symmetry and Rotational symmetry.

Fig.5 Fig. 6

A figure has a line symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide (Fig. 5 & 6)

The concept of line symmetry is closely related to mirror reflection. A shape has line symmetry when one half of it is the mirror image of the other half (Fig 7). A mirror line thus, helps to visualize a Line of symmetry.

Fig.7 If, after a rotation, an object looks exactly the same, we say that it has Rotational Symmetry. There is also a popular advertisement on television in which a bossy like person can be seen finalizing the shape of a snack shaped like an equilateral triangle and looks at it after rotating it at a specific angle and it looks the same and finally finalizes its shape. When an object rotates, its shape and size do not

Fig.8 change. The rotation turns an object about a fixed point. This fixed point is the centre of rotation (see Fig. 9). The angle of turning during rotation is called the angle of rotation (Fig. 10). In a complete turn (of 360o), the number of times an object looks exactly the same is called the order of rotational symmetry (Fig.11). Every object has a rotational symmetry of order 1, as it occupies same position after a rotation of 360° (i.e., one complete revolution).

Fig.9 Fig.10 Fig.11 Harshika also learnt that many plane figures exhibit both symmetries. Even there are some English alphabets that have both symmetries. When she developed more interest in this topic she observed that the idea of symmetry is also being used by designers

,architects and many others in their work. She also saw symmetry in paintings, bed covers, cushions of her house.

She felt proud after knowing that the TAJMAHAL is considered as one of the five most symmetrical objects made by man.

She was amazed to see that even her grandmother is using the idea of symmetry while knitting pullovers. She became more curious to know about the mathematics behind hand knitting.

She also now understands that why her teacher always ask the students to decorate their display board symmetrically. May be, nature as well as we love symmetry.

Now attempt the following questions:

Q1 (A) Draw a rough sketch of two plane figures that have line symmetry as well as rotational symmetry. (2)

(B) Write an English alphabet which has only rotational symmetry (order more than one) and no line symmetry. (1)

(C) Draw a rough sketch of a regular pentagon and its lines of symmetry. (2)

Q2 (a) Give the order of rotational symmetry for each figure given below. (2)

FIG A FIG B(b) What is the angle of rotation and the order of the rotational symmetry for an equilateral triangle? (2)(c) State the number of lines of symmetry for a scalene triangle (1)

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MARKING SCHEME

SA2 2015 16‐ ‐OPEN TEXT BASED ASSESSMENT

CLASS VIIMATHS (THEME 2)‐

NATURE LOVES SYMMETRY

ANS 1.(A) 1 Mark each for correct ans. (square, equilateral triangle or any other)ANS (B) Alphabet S (1 MARK)ANS(C) CORRECT FIG ( 1 MARK) CORRECT LINES OF SYMMETRY ( 1MARK)ANS 2 (a) FIG A 4 1mark FIG B 6 1 mark (b) angle of rotation 120 degree 1 mark order of the rotational symmetry = 3 1 mark (c) 0 1 mark

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