NCERT Solutions for Class 7 Maths Chapter - 14 Symmetry

(a) The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

The name of the figure is square.

(b) The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

The name of the figure is triangle.

(c) The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

The name of the figure is rhombus.

(d) The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

The name of the figure is circle.

(e) The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

The name of the figure is pentagon.

(f) The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

The name of the figure is octagon.

(a)

The figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

(b)

The figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

(c)

The figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

(d)

The figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

(e)

The figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

(f)

The figure given has only 1 line of symmetry.

(g)

The figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

(h)

The figure given has 6 lines of symmetry.

So, it has multiple lines of symmetry.

By observing the above figure,

Yes, the figure will be symmetrical about both diagonals.

By observing the above figure,

Yes, the figure can be made symmetrical in more than one way.

(a)

The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

(b)

The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

(c)

The concept of line of 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. A mirror line, thus helps to visualise a line of symmetry.

While dealing with mirror reflection, care is needed to note down the left-right changes in the orientation.

(a)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

An equilateral triangle which has 3 lines of symmetry is shown in the figure below,

(b)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

An isosceles triangle which has 1 line of symmetry is shown in the figure below,

(c)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A scalene triangle which has no line of symmetry is shown in the figure below,

(d)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A square which has 4 lines of symmetry is shown in the figure below,

(e)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A rectangle which has 2 lines of symmetry is shown in the figure below,

(f)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A rhombus which has 2 lines of symmetry is shown in the figure below,

(g)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A parallelogram which has no line of symmetry is shown in the figure below,

(h)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A quadrilateral which has no line of symmetry is shown in the figure below,

(i)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A regular hexagon which has 6 lines of symmetry is shown in the figure below,

(j)

A figure has a line of symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

A circle which has infinite lines of symmetry,

(a) a vertical mirror

The English letters which have reflection symmetry about a vertical mirror are A, H, I, M, O, T, U, V, W, X, Y

(b) a horizontal mirror

The English letters having reflection symmetry about a horizontal mirror are B, C, D, E, H, I, K, O, X

(c) both horizontal and vertical mirrors

The English alphabet have reflection symmetry about both horizontal and vertical mirrors are, H, I, O, X

A shape has no line of symmetry if there is no line about which the figure may be folded, and parts of the figure will not coincide.

A scalene triangle, a quadrilateral and a parallelogram

(a)

The other name for the line of symmetry of an isosceles triangle is median or altitude.

(b)

The other name for the line of symmetry of a circle is diameter.

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

So, the other hole is shown in the figure below.

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

So, the other hole is shown in the figure below.

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

So, the other hole is shown in the figure below.

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

So, the other hole is shown in the figure below.

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

So, the other hole is shown in the figure below.

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

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

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

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

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

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

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

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

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

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

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

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

(a)

The above figure has rotational symmetry of order 2.

(b)

The above figure has rotational symmetry of order 2.

(c)

The above figure has rotational symmetry of order 3.

(d)

The above figure has rotational symmetry of order 4.

(e)

The above figure has rotational symmetry of order 4.

(f)

The above figure has rotational symmetry of order 5.

(g)

The above figure has rotational symmetry of order 6.

(h)

The above figure has rotational symmetry of order 3.

(a)

So, the above figure has rotational symmetry of order 4.

(b)

So, the above figure has rotational symmetry of order 3.

(c) So, the given figure has rotational symmetry of order 1.

(d)

So, the above figure has rotational symmetry of order 2.

(e)

So, the above figure has rotational symmetry of order 3.

(f)

So, the above figure has rotational symmetry of order 4.

By observing all the figures (a), (b), (c), (d), (e) and (f) have rotational symmetry of order more than 1.

The other angles are, 120°, 180°, 240°, 300°, 360°

So, the figure is said to have rotational symmetry about the same angle as the first one. Hence, the figure will look exactly the same when rotated by 60° from the last position.

Equilateral triangle and Circle.

Yes. If a figure has two or more lines of symmetry, then it will have rotational symmetry of order more than 1.

The quadrilateral, which has both line and rotational symmetry of order more than 1, is a square.

Line symmetry:

Rotational symmetry:

(i) A triangle with both line and rotational symmetries of order more than 1 is an equilateral triangle.

Line symmetry

Rotational symmetry

(ii) A triangle with only line symmetry and no rotational symmetry of order more than 1 is an isosceles triangle.

(iii) A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry is not possible to draw. Because a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.

(iv) A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is a rhombus.

(i) Yes. We can have a rotational symmetry of order more than 1 whose angle of rotation is 45o.

(ii) No. We cannot have a rotational symmetry of order more than 1 whose angle of rotation is 17o.