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#### Page No 17.11:

#### Question 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) Square | ||

(vi) Parallelogram | ||

(vii) Rhombus | ||

(viii) Line | ||

(ix) Line segment | ||

(x) Angle | ||

(xi) Isosceles trepezium | ||

(xii) Kite | ||

(xiii) Arrow-head | ||

(xiv) Semi-circle | ||

(xv) Circle | ||

(xvi) Regular pentagon | ||

(xvii) Regular hexagon |

#### Answer:

Shapes |
Rough Figure |
Number of lines of symmetry |

(i) Scalene triangle | 0 | |

(ii) Isosceles triangle | 1 | |

(iii) Equilateral triangle | 3 | |

(iv) Rectangle | 2 | |

(v) Square | 4 | |

(vi) 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 |

#### Page No 17.12:

#### Question 2:

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

(i) vertical line of symmetry. (like A)

(ii) horizontal lines of symmetry. (like B)

(iii) vertical and horizontal lines of symmetry. (like I)

(iv) no line of symmetry. (like Q)

#### Answer:

(i)

(ii)

(iii)

(iv)

#### Page No 17.12:

#### Question 3:

Can you draw a triangle having:

(i) exactly one line of symmetry.

(ii) exactly two lines of symmetry.

(iii) three lines of symmetry.

(iv) no line of symmetry.

#### Answer:

(i) Yes; isosceles triangle

(ii) No

(iii) Yes; equilateral triangle

(iv) Yes; scalene triangle

#### Page No 17.12:

#### Question 4:

On a squared paper, sketch the following:

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

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

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

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

(v) A hexagon with six lnes of symmetry.

#### Answer:

(i)

(ii)

(iii)

(iv)

(v)

#### Page No 17.12:

#### Question 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.

#### Answer:

#### Page No 17.12:

#### Question 6:

Write the specific names of all the three quadrilaterals which have only one line of symmetry.

#### Answer:

#### Page No 17.12:

#### Question 7:

Trace each of the following figures and draw the lines of symmetry, if any:

#### Answer:

#### Page No 17.13:

#### Question 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.

#### Answer:

(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 because it has only one line of symmetry.

#### Page No 17.13:

#### Question 9:

Find the lines of symmetry for each of the following:

#### Answer:

#### Page No 17.13:

#### Question 10:

State whether the following statements are true of false:

(i) A right-angled triangle can have at most one line of symmetry.

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

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

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

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

(vi) a hexagon with more than two lines of symmetry must be regular.

#### Answer:

(i) True

If it is an Isosceles right-angled triangle, then it can have only one line of symmetry at the most. Otherwise, a right-angled triangle has no line of symmetry.

(ii) True

If an Isosceles triangle has 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.

Isosceles triangle Equilateral triangle

(iii) True

(iv) True

(v) True

(vi) True

#### Page No 17.14:

#### Question 1:

The total number of lines of symmetry of a scalene triangle is

(a) 1

(b) 2

(c) 3

(d) None of these

#### Answer:

(d) None of these

This is because the line of symmetry of a Scalene triangle is 0.

#### Page No 17.14:

#### Question 2:

The total number of lines of symmetry of an isosceles triangle is

(a) 1

(b) 2

(c) 3

(d) None of these

#### Answer:

(a) 1

#### Page No 17.14:

#### Question 3:

An equilateral triangle is symmetrical about each of its

(a) altitudes

(b) medians

(c) angle bisectors

(d) all the above

#### Answer:

(d) all the above

In an equilateral triangle altitudes, angle bisectors and medians are all the same.

#### Page No 17.14:

#### Question 4:

The total number of lines of symmetry of a square is

(a) 1

(b) 2

(c) 3

(d) 4

#### Answer:

(d) 4

#### Page No 17.14:

#### Question 5:

A rhombus is symmetrical about

(a) each of its diagonals

(b) the line joining the mid-points of its opposite sides

(c) perpendicular bisectors of each of its sides

(d) none of these

#### Answer:

(a) Each of its diagonals

#### Page No 17.14:

#### Question 6:

The number of lines of symmetry of a rectangle is

(a) 0

(b) 2

(c) 4

(d) 1

#### Answer:

(b) 2

#### Page No 17.14:

#### Question 7:

The number of lines of symmetry of a kite is

(a) 0

(b) 1

(c) 2

(d) 3

#### Answer:

(b) 1

#### Page No 17.14:

#### Question 8:

The number of lines of symmetry of a circle is

(a) 0

(b) 1

(c) 4

(d) unlimited

#### Answer:

(d) Unlimited

A circle has an infinite number of lines of symmetry all along the diameters. It has an infinite number of diameters.

#### Page No 17.14:

#### Question 9:

The number of lines of symmetry of a regular hexagon is

(a) 1

(b) 3

(c) 6

(d) 8

#### Answer:

(c) 6

#### Page No 17.14:

#### Question 10:

The number of lines of symmetry of an *n*-sided regular polygon is

(a) *n*

(b) 2*n*

(c) $\frac{n}{2}$

(d) none of these

#### Answer:

(a) n

The number of lines of symmetry of a regular polygon is equal to the sides of the polygon. If it has 'n' number of sides, then there are 'n' lines of symmetry.

#### Page No 17.14:

#### Question 11:

The number of lines of symmetry of the letter *O* of the English alphabet is

(a) 0

(b) 1

(c) 2

(d) 3

#### Answer:

(c) 2

#### Page No 17.14:

#### Question 12:

The number of lines of symmetry of the letter *Z* of the English alphabet is

(a) 0

(b) 1

(c) 2

(d) 3

#### Answer:

(a) 0

Z has no line of symmetry.

#### Page No 17.4:

#### Question 1:

List any four symmetrical objects from your home or school. Also mention the line of symmetry.

#### Answer:

1. A gate -

2. A Green-board -

3. A pair of spectacles -

4. A glass -

#### Page No 17.4:

#### Question 2:

Identify the symmetrical instruments from your mathematical instrument box.

#### Answer:

1. A protractor

2. A divider

3. A ruler (scale)

4. An eraser

5. A pencil

#### Page No 17.4:

#### Question 3:

Copy each of the following on a squared paper and compute them in such a way that the dotted line is the line of symmetry.

#### Answer:

#### Page No 17.5:

#### Question 1:

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

#### Answer:

#### Page No 17.5:

#### Question 2:

Copy the following drawings on squared paper and complete each one of them in scuh a way that resulting figure has two dotted lines as two lines of symmetry:

#### Answer:

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