Exercise 14.1 Page: 268

**1. Copy the figures with punched holes and find the axes of symmetry for the following:**

**(a)**

**Solution:-**

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)**

**Solution:-**

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)**

**Solution:-**

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)**

**Solution:-**

**(e)**

**Solution:-**

**(f)**

**Solution:-**

**(g)**

**Solution:-**

**(h)**

**Solution:-**

**(i)**

**Solution:-**

**(j)**

**Solution:-**

**(k)**

**Solution:-**

**(l)**

**Solution:-**

**2. Given the line(s) of symmetry, find the other hole(s):**

**(a)**

**Solution:-**

So, other hole is shown in the figure below.

**(b)**

**Solution:-**

So, other hole is shown in the figure below.

**(c)**

**Solution:-**

So, other hole is shown in the figure below.

**(d)**

**Solution:-**

So, other hole is shown in the figure below.

**(e)**

**Solution:-**

So, other hole is shown in the figure below.

**3. In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete?**

**(a)**

**Solution:-**

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.

Name of the figure is square.

**(b)**

**Solution:-**

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.

Name of the figure is triangle.

**(c)**

**Solution:-**

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.

Name of the figure is rhombus.

**(d)**

**Solution:-**

Name of the figure is circle.

**(e)**

**Solution:-**

Name of the figure is pentagon.

**(f)**

**Solution:-**

Name of the figure is octagon.

**4. The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.**

**Identify multiple lines of symmetry, if any, in each of the following figures:**

**(a)**

**Solution:-**

Figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

**(b)**

**Solution:-**

Figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

**(c)**

**Solution:-**

Figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

**(d)**

**Solution:-**

Figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

**(e)**

**Solution:-**

Figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

**(f)**

**Solution:-**

Figure given has only 1 line of symmetry.

**(g)**

**Solution:-**

Figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

**(h)**

**Solution:-**

Figure given has 6 lines of symmetry.

So, it has multiple lines of symmetry.

**5. Copy the figure given here.**

**Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?**

**Solution:-**

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 by more than one way.

**6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):**

**(a)**

**Solution:-**

**(b)**

**Solution:-**

**(c)**

**Solution:-**

**7. State the number of lines of symmetry for the following figures:**

**(a) An equilateral triangle**

**Solution:-**

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

**(b) An isosceles triangle**

**Solution:-**

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

**(c) A scalene triangle**

**Solution:-**

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

**(d) A square**

**Solution:-**

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

**(e) A rectangle**

**Solution:-**

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

**(f) A rhombus**

**Solution:-**

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

**(g) A parallelogram**

**Solution:-**

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

**(h) A quadrilateral**

**Solution:-**

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

**(i) A regular hexagon**

**Solution:-**

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

**(j) A circle**

**Solution:-**

A circle has infinite lines of symmetry,

**8. What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about.**

**(a) a vertical mirror (b) a horizontal mirror**

**(c) both horizontal and vertical mirrors**

**Solution:-**

**(a)** a vertical mirror

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

**9. Give three examples of shapes with no line of symmetry.**

**Solution:-**

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

A scalene triangle, a quadrilateral and a parallelogram

**9. Give three examples of shapes with no line of symmetry.**

**Solution:-**

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

A scalene triangle, a quadrilateral and a parallelogram

**10. What other name can you give to the line of symmetry of**

**(a) an isosceles triangle?**

**Solution:-**

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

**(b) a circle?**

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