**NCERT Solutions Class 9 Maths Chapter 5 Introduction To Euclids Geometry** – Here are all the NCERT solutions for Class 9 Maths Chapter 5. This solution contains questions, answers, images, explanations of the complete Chapter 5 titled Introduction To Euclids Geometry of Maths taught in class 9. If you are a student of class 9 who is using NCERT Textbook to study Maths, then you must come across Chapter 5 Introduction To Euclids Geometry. After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 9 Maths Chapter 5 Introduction To Euclids Geometry in one place.

## NCERT Solutions Class 9 Maths Chapter 5 Introduction To Euclids Geometry

Here on **AglaSem Schools**, you can access to **NCERT Book Solutions** in free pdf for Maths for Class 9 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 5 Introduction To Euclids Geometry , Maths, Class 9.

Class | 9 |

Subject | Maths |

Book | Mathematics |

Chapter Number | 5 |

Chapter Name |
Introduction To Euclids Geometry |

### NCERT Solutions Class 9 Maths chapter 5 Introduction To Euclids Geometry

Class 9, Maths chapter 5, Introduction To Euclids Geometry solutions are given below in PDF format. You can view them online or download PDF file for future use.

### Introduction To Euclids Geometry

**NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Download**

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### NCERT Solutions Class 9 Maths chapter 5 Introduction To Euclids Geometry- Video

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### Question & Answer

Q.1: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 Fig, if AB = PQ and PQ = XY, then AB = XY.

Ans :(i) False. Since through a single point, infinite number of lines can pass. In the following figure, it can be seen that there are infinite numbers of lines passing through a single point P. (ii) False. Since through two distinct points, only one line can pass. In the following figure, it can be seen that there is only one single line that can pass through two distinct points P and Q. (iii) True. A terminated line can be produced indefinitely on both the sides. Let AB be a terminated line. It can be seen that it can be produced indefinitely on both the sides. (iv)True. If two circles are equal, then their centre and circumference will coincide and hence, the radii will also be equal. (v) True. It is given that AB and XY are two terminated lines and both are equal to a third line PQ. Euclid's first axiom states that things which are equal to the same thing are equal to one another. Therefore, the lines AB and XY will be equal to each other.

Q.2:Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them? (i) parallel lines (ii) perpendicular lines (iii) line segment (iv) radius of a circle (v) square

Ans :(i)Parallel LinesIf the perpendicular distance between two lines is always constant, then these are called parallel lines. In other words, the lines which never intersect each other are called parallel lines.To define parallel lines, we must know about point, lines, and distance between the lines and the point Of intersection. (ii)Perpendicular linesIf two lines intersect each other at 90°, then these are called perpendicular lines. We are required to define line and the angle before defining perpendicular lines. (iii)Line segmentA straight line drawn from any point to any other point is called as line segment. To define a line segment, we must know about point and line segment. (iv)Radius of a circleIt is the distance between the centres of a circle to any point lying on the circle. To define the radius of a circle, we must know about point and circle. (v)SquareA square is a quadrilateral having all sides Of equal length and all angles Of same measure, I.e., 90° • To define square, we must know about quadrilateral, side, and angle.

Q.3: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.

Ans :There are various undefined terms in the given postulates. The given postulates are consistent because they refer to two different situations. Also, it is impossible to deduce any statement that contradicts any well known axiom and postulate. These postulates do not follow from Euclid's postulates. They follow from the axiom, "Given two distinct points, there is a unique line that passes through them".

Q.4:If a point C lies between two points A and B such that AC = BC, then prove that AC \(=\frac{1}{2} \mathrm{AB}\). Explain by drawing the figure.

Ans :It is given that, AC = BC Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another. It is also known that things which are equal to the same thing are equal to one another. Therefore, from equations (1) and (2), we obtain AC+AC = AB 2AC = AB \(\therefore \mathrm{AC}=\frac{1}{2} \mathrm{AB}\)

Q.5:In Question 4, point C is called a midpoint of line segment AB. Prove that every line segment has one and only one midpoint.

Ans :AC = CB AC+AC= BC+AC (Equals are added on both sides) …….(1) Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another. Therefore BC + AC = AB ……(2) It is also known that things which are equal to the same thing are equal to one another. Therefore, from equations (1) and (2), we obtain AC + AC = AB 2AC = AB….. (3) Similarly, by taking D as the midpoint of Ad, it can be proved that 2AD = AB…. (4) From equation (3) and (4), we obtain 2AC = 2AD (Things which are equal to the same thing are equal to One another.) AC = AD (Things which are double of the same things are equal to one another.) This is possible only when point C and D are representing a single point. Hence, our assumption is wrong and there can be only one mid-point of a given line Segment.

## NCERT / CBSE Book for Class 9 Maths

You can download the NCERT Book for Class 9 Maths in PDF format for free. Otherwise you can also buy it easily online.

- Click here for NCERT Book for Class 9 Maths
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### All NCERT Solutions Class 9

- NCERT Solutions for Class 9 English
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