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NCERT solutions Mathematics Textbook for Class 9 chapter 5 Introduction to Euclid's Geometry

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Chapter 5 - Introduction to Euclid's Geometry

Pages 85 - 86

Which of the following statements are true and which are false? Give reasons for your answers.

(i) Only one line can pass through a single point.

(ii) There are an infinite number of lines which pass through two distinct points.

(iii) A terminated line can be produced indefinitely on both the sides.

(iv) If two circles are equal, then their radii are equal.

(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY

Q 1 | Page 85 |

Give a definition for parallel lines. Are there other terms that need to be defined first? What are they, and how might you define them?

Q 2.1 | Page 85 |

Give a definition for perpendicular lines. Are there other terms that need to be defined first? What are they, and how might you define them?

Q 2.2 | Page 85 |

Give a definition for line segment. Are there other terms that need to be defined first? What are they, and how might you define them?

Q 2.3 | Page 85 |

Give a definition for radius of a circle. Are there other terms that need to be defined first? What are they, and how might you define them?

Q 2.4 | Page 85 |

Give a definition for square. Are there other terms that need to be defined first? What are they, and how might you define them?

Q 2.5 | Page 85 |

Consider two ‘postulates’ given below:-

(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.

(ii) There exist at least three points that are not on the same line.

Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.

Q 3 | Page 85 |

If a point C lies between two points A and B such that AC = BC, then prove that Ac =  1/2AB. Explain by drawing the figure.

Q 4 | Page 86 |

If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

Q 5 | Page 86 |

In the following figure, if AC = BD, then prove that AB = CD.

Q 6 | Page 86 |

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

Q 7 | Page 86 |

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