### Exercise 17.3

**1. Complete the following table:**

Shapes | Rough figure | Number of lines of symmetry |

(i) scalene triangle | 0 | |

(ii) Isosceles triangle | 1 | |

(iii) equilateral triangle | ||

(iv) Rectangle | ||

(v) Parallelogram | ||

(vii) Rhombus | ||

(viii) Line | ||

(ix) Line segment | ||

(x) Angle | ||

(xi) Isosceles trapezium | ||

(xii) Kite | ||

(xiii) Arrow head | ||

(xiv) Semi – circle | ||

(xv) Circle | ||

(xvi) Regular pentagon | ||

(xvii) Regular hexagon |

**Soln:**

Shapes | Rough figure | Number of lines of symmetry |

(i) scalene triangle | 0 | |

(ii) Isosceles triangle | 1 | |

(iii) equilateral triangle | 3 | |

(iv) Rectangle | 4 | |

(v) Parallelogram | 0 | |

(vii) Rhombus | 2 | |

(viii) Line | Infinitely many | |

(ix) Line segment | 1 | |

(x) Angle | 1 | |

(xi) Isosceles trapezium | 1 | |

(xii) Kite | 1 | |

(xiii) Arrow head | 1 | |

(xiv) Semi – circle | 1 | |

(xv) Circle | Infinitely many | |

(xvi) Regular pentagon | 5 | |

(xvii) Regular hexagon | 6 |

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

i. Vertical line of symmetry

ii. Horizontal line of symmetry

iii. Vertical and Horizontal line of symmetry

iv. No line of symmetry

**3. Can you draw a triangle having?**

i. Exactly one line of symmetry.

Ans: Yes; isosceles triangle

ii. Exactly two line of symmetry.

Ans: No

iii. Three line of symmetry.

Ans: Yes; equilateral triangle

iv. no lines of symmetry

ans: Yes; scalene triangle

**4. On a squared paper, sketch the following **

i. A triangle with a horizontal with both horizontal and vertical line of symmetry

ii. A quadrilateral with both horizontal and vertical lines of symmetry

Iii. A quadrilateral with horizontal but no vertical lines of symmetry

iv. A hexagon with exactly two lines of symmetry

v. A hexagon with exactly six lines of symmetry

**5. Draw neat diagrams showing the line (or lines) of symmetry and give the specific name to the quadrilateral having:**

i. only one line of symmetry. How many such quadrilaterals are there?

ii. its diagonals as the only lines of symmetry

iii. two lines of symmetry other than diagonals

iv. More than two lines of symmetry

**6. write the specific names of all the three quadrilaterals which have only one line of symmetry **

**7. Trace each of the following figures and draw the lines of symmetry. If any**

i.

ii.

iii.

iv.

v.

vi.

**8. On squared paper copy the triangle in each of the following figures. In each case draw the line(s) of symmetry if any and identify the type of the triangle**

(i) This is an isosceles triangle because it has only one line of symmetry.

(ii) This is an Equilateral triangle because it has three lines of symmetry.

(iii) This is a right angled triangle because it has no line of symmetry.

(iv) This is an isosceles triangle it has one line of symmetry.

**9. Find the lines of symmetry for each of the following shapes**

i.

ii.

iii.

iv.

v.

vi.

vii.

viii.

**10. State whether the following statements are true or false:**

(i) A right- angled triangle can have at most two lines of symmetry

A : True

If it is an isosceles right angle triangle, then it can have only one line of symmetry at the most.

Otherwise, a right angle triangle has no line of symmetry.

(ii) An isosceles triangle with more than one line of symmetry must be an equilateral triangle

A: If an isosceles triangle has no more than one line of symmetry, then it must be an equilateral triangle.

This is because an equilateral triangle has three lines of symmetry, and a triangle other than that cannot have two lines of symmetry.

iii. A pentagon with one line of symmetry can be drawn.

A: True

iv. A pentagon with more than one line of symmetry must be regular

A: True

v. A hexagon with one line of symmetry can be drawn

A: True

vi. A hexagon with more than one line of symmetry must be regular

A: True