### Symmetry - Solutions

CBSE Class –VII Mathematics

NCERT Solutions

Chapter 14 Symmetry (Ex. 14.1)

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

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

Answer: Sol.

S.No. | Punched holed figures | The axes of symmetry |

(a) | (rectangle) | |

(b) | ||

(c) | ||

(d) | ||

(e) | ||

(f) | ||

(g) | ||

(h) | ||

(i) | ||

(j) | ||

(k) | ||

(l) |

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

S.No. | Line(s) of symmetry | Other holes on figures |

(a) | ||

(b) | ||

(c) | ||

(d) | ||

(e) |

Ans.

S.No. | Line(s) of symmetry | Other holes on figures |

(a) | ||

(b) | ||

(c) | ||

(d) | ||

(e) |

Question 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?

Answer: Sol.

S.No. | Question figures | Complete figures | Names of the figure |

(a) | Square | ||

(b) | Triangle | ||

(c) | Rhombus | ||

(d) | Circle | ||

(e) | Pentagon | ||

(f) | Octagon |

Question 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:

Answer:

S.No. | Problem Figures | Lines of symmetry |

(a) | ||

(b) | ||

(c) | ||

(d) | ||

(e) | ||

(f) | ||

(g) | ||

(h) |

Question 5. Copy the figure given here:

Answer figures are:

Yes, there is more than one way.

Yes, this figure will be symmetric about both the diagonals.

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

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

Answer:

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

(a) An equilateral triangle(b) An isosceles triangle(c) A scalene triangle

(d) A square(e) A rectangle(f) A rhombus

(g) A parallelogram(h) A quadrilateral(i) A regular hexagon

(j) A circle

Answer:

S.No. | Figure’s name | Diagram with symmetry | Number of lines |

(a) | Equilateral triangle | 3 | |

(b) | Isosceles triangle | 1 | |

(c) | Scalene triangle | 0 | |

(d) | Square | 4 | |

(e) | Rectangle | 2 | |

(f) | Rhombus | 2 | |

(g) | Parallelogram | 0 | |

(h) | Quadrilateral | 0 | |

(i) | Regular Hexagon | 6 | |

(j) | Circle | Infinite |

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

1. a vertical mirror

2. a horizontal mirror

3. both horizontal and vertical mirrors

Answer: (a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y mirror mirror

(b) Horizontal mirror – B, C, D, E, H, I, O and X

(c) Both horizontal and vertical mirror – H, I, O and X

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

Answer: The three examples are:

1. Quadrilateral

2. Scalene triangle

3. Parallelogram

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

1. an isosceles triangle?

2. a circle?

Answer: (a) The line of symmetry of an isosceles triangle is median or altitude.

(b) The line of symmetry of a circle is diameter.