Page 211 - ICSE Math 7

9. A soft toy manufacturing company designs two samples for a toy of butterfly as shown.

A B
Use the concept of symmetry to identify the sample which is good for the market.

THINK SMART

1. After rotating about the centre at 45°, a figure looks exactly the same as it appeared at its original
position. At what other angles will the figure look exactly the same?

2. Estimate the angle of rotation about O in clockwise direction in which each figure should go
through to attain a new position as shown.

O
(a) (b)
O O
O

(c) O O (d) O O

Maths Lab Activity

Objective: To find the rotational symmetry of a parallelogram
Step 1: Draw a parallelogram on a white sheet of paper.
Step 2: Draw an identical parallelogram on a tracing paper. Obtain a cutout of the parallelogram
from the tracing paper and place it on the parallelogram drawn on the white sheet.
Step 3: Put a pin at O, the point of intersection of the diagonals. Before putting the pin ensure
the cutout of the parallelogram coincide with the one drawn on the white sheet. Put an
arrow mark on the diagonal near the vertex.

180° 180°
O O O

Step 4: Now turn the parallelogram drawn on the tracing paper in clockwise direction. On
rotation through 180°, we observe that the two parallelograms coincide.
Step 5: After one more rotation of 180°, the parallelogram regains its original position once

again. [See position of arrow on the diagonal.]
Inference: Since in a full turn, on rotation of 180° and 360° the parallelogram looks exactly the
same, we conclude that the parallelogram has rotational symmetry of order 2.

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