**Exercise 13.1**

Ex 13.1 Class 6 Maths Question 1.

List any four symmetrical objects from your home or school.

Solution:

The following objects can be symmetrical:

(a) Notebook

(b) Dinning table

(c) A blackboard

(d) Wall clock

(e) A pair of scissors

Ex 13.1 Class 6 Maths Question 2.

For the given figure, which one is the mirror line, l^{1} or l^{2}?

Solution:

In the following figure, l^{2} is the mirror line.

Ex 13.1 Class 6 Maths Question 3.

Identify the shapes given below. Check whether they are symmetrical or not. Draw the line of symmetry as well.

Solution:

(a) The given symmetric figure is a lock in which vertical line ‘l’ is the line of symmetry.

(b) The given figure is a symmetrical bucket in which vertical line ‘l’ is the line of symmetry.

(c) The given figure is not symmetrical.

(d) The given figure is a symmetric telephone in which vertical line l is called the line of symmetry.

(e) The given figure is symmetrical. Horizontal line l is called the line of symmetry.

(f) The given figure is symmetrical. Vertical line l is called its line of symmetry.

Ex 13.1 Class 6 Maths Question 4.

Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook is earlier classes. Then complete them such that the dotted line is the line of symmetry.

Solution:

Ex 13.1 Class 6 Maths Question 5.

In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.

Solution:

The completed figure is as follows:

Ex 13.1 Class 6 Maths Question 6.

In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.

Solution:

The symmetric figure is given as follows.

**Exercise 13.2**

Ex 13.2 Class 6 Maths Question 1.

Find the number of lines of symmetry for each of the following shapes.

Solution:

(a) Here, there are four symmetric lines l, m, n and o.

(b) In this figure, there are four symmetric lines p, q, r and s.

(c) In this shape, u, v , w and x are four lines of symmetry.

(d) In this shape only m is the line of symmetry.

(e) Here, a, b, c, d, e and fare six lines of symmetry.

(f) In this figure l, m, n, o, p and q are six lines of symmetry.

(g) This figure has no lines of symmetry.

(h) This figure has no lines of symmetry.

(i) This figure has five lines of symmetry.

Ex 13.2 Class 6 Maths Question 2.

Copy the triangle in each of the figures on squared paper. In each case, draw the line(s) of symmetry, if any and identify the type of triangle. (Some of you may like to trace the figures and try paper-folding first!)

Solution:

(a) It is an isosceles triangle having one symmetric line.

(b) This figure is an isosceles triangle having only one symmetric line.

(c) It is an isosceles right angled triangle which has only one symmetric line.

(d) It is a scalene triangle. It has no symmetric line.

Ex 13.2 Class 6 Maths Question 3.

Complete the following table.

Shape | Rough figure | Number of lines of symmetry |

Equilateral triangle | 3 | |

Square | ||

Rectangle | ||

Isosceles triangle | ||

Rhombus | ||

Circle |

Solution:

Completed table:

Shape | Rough figure | Number of lines of symmetry |

(a) Equilateral triangle | 3 | |

(b) Square | 4 | |

(c) Rectangle | 2 | |

(d) Isosceles triangle | 1 | |

(e) Rhombus | 2 | |

(f) Circle | Infinite |

Ex 13.2 Class 6 Maths Question 4.

Can you draw a triangle which has

(a) exactly one line of symmetry?

(b) exactly two lines of symmetry?

(c) exactly three lines of symmetry?

(d) no lings of symmetry?

Sketch a rough figure in each case.

Solution:

(a) Yes, Isosceles right angled triangle has exactly one line of symmetry.

(b) No, we cannot draw any triangle with two symmetric lines.

(c) Yes, equilateral triangle has three lines of symmetry.

(d) Yes, Scalene triangle has no lines of symmetry

Ex 13.2 Class 6 Maths Question 5.

On a squared paper, sketch the following:

(а) A triangle with a horizontal line of symmetry but no vertical line of symmetry.

(b) A quadrilateral with both horizontal and vertical lines of symmetry.

(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

(d) A hexagon with exactly two lines of symmetry.

(e) A hexagon with six lines of symmetry. (Hint: It will be helpful if you first draw the lines of symmetry and then complete the figures)

Solution:

(a) The figure shows an isosceles triangle with horizontal line of symmetry.

(b) Rectangle (quadrilateral) shows both the horizontal and vertical lines of symmetry.

(c) Trapezium (quadrilateral) shows the horizontal but no vertical line of symmetry.

(d) The hexagon drawn below shows only two lines of symmetry.

(e) The regular hexagon shows the six lines of symmetry.

Ex 13.2 Class 6 Maths Question 6.

Trace each figure and draw the lines of symmetry, if any.

Solution:

(a) The given figure has no line of symmetry as it is not symmetrical.

(b) The given figure has two lines of symmetry.

(c) The given figure has four lines of symmetry.

(d) The given figure has two lines of symmetry.

(e) This figure has only one horizontal line of symmetry.

(f) The given figure has two lines of symmetry.

Ex 13.2 Class 6 Maths Question 7.

Consider the letters of English alphabets A to Z. List among them the letters which have

(a) vertical lines of symmetry, (like A)

(b) horizontal lines of symmetry (like B)

(c) no lines of symmetry, (like Q)

Solution:

(a) The following letters have vertical lines of symmetry:

A, H, I, M, O, T, U, V, W, X, and Y

(b) The following letters have horizontal lines of symmetry:

B, C, D, E, H, I, K, O and X.

(c) The following letters have no lines of symmetry:

F, G, J, L, N, P, Q, R, S and Z.

Ex 13.2 Class 6 Maths Question 8.

Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.

Solution:

The given figures will be seen as follows when they are completed.

**Exercise 13.3**

Ex 13.3 Class 6 Maths Question 1.

Find the number of lines of symmetry in each of the following shapes. How will you check your answer?

Solution:

(a) The given figure has 4 lines of symmetry.

(b) The given figure has only one line of symmetry.

(c) The given figure has two line of symmetry.

(d) The given figure has two lines of symmetry.

(e) This figure has only one line of symmetry.

(f) The given figure has two lines of symmetry.