Page 255 - Start Up Mathematics_6

Forming 5-Digit Numbers

MATHS LAB ACTIVITY

Fun with Symmetry

Take a rectangular sheet of paper.
Fold it from the middle along the dotted line
as shown in figure (i).
Next fold it again along the dotted line as (i) (ii) (iii)
shown in figure (ii).

Now cut a curved piece from the corner as shown in figure (iii). Unfold the paper. Can you see
a design.
Predict all the lines of symmetry of the design before unfolding the paper. Check your answer
after unfolding it. Make some more designs using this method.

At a Glance

1. A figure is symmetrical about a line if it divides the figure into two identical parts. The line
about which a figure is symmetrical is called the line or axis of symmetry.
2. All figures are not symmetrical. A figure may not have any line of symmetry. Some figures may
have one, two or more than two lines of symmetry. A parallelogram has no line of symmetry,
an isosceles triangle has 1 line, a rhombus has 2 lines, an equilateral triangle has 3 lines, a
regular hexagon has 6 lines and a circle has infinite lines of symmetry.
3. Mirror reflection is closely related to line symmetry. The mirror line acts as a line of symmetry.
The figure and its image are exactly identical but there is left-right changes in orientation,
i.e., the image is laterally inverted.

Review Exercises

Multiple ChoiCe Questions
1. The number of lines of symmetry of a regular octagon is:

(a) 4 (b) 6 (c) 7 (d) 8
2. A geometrical figure and its corresponding mirror image are:
(a) congruent (b) similar (c) laterally inverted (d) all the above

3. A rhombus is symmetrical about:
(a) each of its diagonals
(b) the line joining the midpoint of the opposite sides

(c) the perpendicular bisector of its sides
(d) its altitude from the vertex to the opposite side
4. The number of lines of symmetry which a triangle cannot have is:

(a) 0 (b) 1 (c) 2 (d) 3
5. The angle between the mirror line l and the line segment joining a point and its image is:
(a) 0° (b) 45° (c) 90° (d) 120°

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