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**Introduction to Euclids Geometry Class 9 Questions And Answers **are provided here. These NCERT solutions are designed by expert team considering latest CBSE syllabus 2023-24 and to provide comprehensive coverage of concepts to students which ultimately help in the exam. This class 9 NCERT syllabus chapter will discuss Euclid’s approach to geometry and its real-life applications. Here you will get NCERT solutions for class 9 maths also.

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This Story also Contains

- NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclids Geometry
- Introduction to Euclids Geometry Class 9 Questions And Answers PDF Free Download
- Introduction to Euclids Geometry Class 9 Solutions - Important Points
- Introduction to Euclids Geometry Class 9 NCERT Solutions (Intext Questions and Exercise)
- NCERT Solutions For Class 9 chapter 5 - Topics
- Key Features of Class 9 Introduction To Euclids Geometry NCERT Solutions
- NCERT Solutions For Class 9 - Chapter Wise
- NCERT Solutions For Class 9 - Subject Wise
- NCERT Books and NCERT Syllabus

This Introduction to euclids geometry class 9 solutions includes two exercises with 9 questions. NCERT solutions for class 9 maths chapter 5 Introduction to Euclid’s Geometry consist of detailed explanations for all the 9 questions. This chapter talks about the basic observation of geometry which is generally ignored by the students. Introduction to Euclids geometry class 9 NCERT solutions is covering each and every single step to answer the practice exercise questions. In this chapter, you will study definitions like a point, a line, and a plane which are defined by Euclid’s and Euclid’s five postulates.

**Also Read :**

- NCERT Exemplar Solutions For Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry
- Introduction To Euclid's Geometry Class 9 Chapter Note

**>> Axioms:**

Equality Axiom: If two things are equal to the same thing, they are equal to each other.

Addition Axiom: If equals are added to equals, the wholes are equal.

Subtraction Axiom: If equals are subtracted from equals, the remainder are equal.

Coincidence Axiom: Things which coincide with one another are equal to one another.

Whole-Part Axiom: The whole is greater than the part.

**>> Postulates (Euclid's five postulates):**

Postulate of Straight Lines: A straight line can be drawn from any one point to any other point.

Postulate of Line Extension: A terminated line can be produced indefinitely.

Postulate of Circle Drawing: A circle can be drawn with any centre and any radius.

Postulate of Right Angles: All right angles are equal to one another.

Postulate of Parallel Lines: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

Free download **NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclids Geometry **for CBSE Exam.

**Class 9 maths chapter 5 question answer Excercise: 5.1** ** **

**Q1 ** 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. 5.9, if AB = PQ and PQ = XY, then AB = XY.

** Answer: **

i) ** FALSE **

Because there is the infinite number of lines that can be passed through a single point. As shown in the diagram below

ii) ** FALSE **

Because only one line can pass through two distinct points. As shown in the diagram below

iii) ** TRUE **

Because a terminated line can be produced indefinitely on both sides. As shown in the diagram below

iv) ** TRUE **

Because if two circles are equal, then their centre and circumference will coincide and hence, the radii will also be equal.

v) ** TRUE **

By Euclid’s first axiom things which are equal to the same thing, are equal to one another

** Answer: **

Yes, there are other terms that are needed to be defined first which are:

Plane: A plane is a flat surface on which geometric figures are drawn.

Point: A point is a dimensionless dot which is drawn on a plane surface.

Line: A line is the collection of n number of points which can extend in both the directions and has only one dimension.

i) Parallel line:-

If the perpendicular distance between two lines is always constant and they never intersect with each other in a plane. Then, two lines are called parallel lines.

** Answer: **

Yes, there are other terms that are needed to be defined first which are:

Plane: A plane is a flat surface on which geometric figures are drawn.

Point: A point is a dimensionless dot which is drawn on a plane surface.

Line: A line is the collection of n number of points which can extend in both the directions and has only one dimension.

ii) perpendicular line:-

If two lines intersect with each other and make a right angle at the point of intersection. Then, two lines are called perpendicular lines.

** Answer: **

Yes, there are other terms that are needed to be defined first which are:

Plane: A plane is a flat surface on which geometric figures are drawn.

Point: A point is a dimensionless dot which is drawn on a plane surface.

Line: A line is collection of n number of points which can extend in both the directions and has only one dimension.

iii) line segment : -

A straight line with two end points that cannot be extended further and has a definite length is called line segment

** Answer: **

iv) Radius of the circle : -

The distance between the centre of the circle and any point on the circumference of the circle is called the radius of a circle.

** Q2 (v) ** 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? v) square

** Answer: **

v) Square:-

A square is a quadrilateral in which all the four sides are equal and each internal angle is a right angle.

To define the square, we must know about quadrilateral.

** Q3 ** 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.

** Answer: **

There are various undefined terms in the given postulates.:

1) There is no information given about the plane whether the points are in the same plane or not.

2) There is the infinite number of points lie in a plane. But here the position of the point C has not specified whether it lies on the line segment joining AB or not.

Yes, these postulates are consistent when we deal with these two situations:

(i) Point C is lying in between and on the line segment joining A and B.

(ii) Point C does not lie on the line segment joining A and B.

No, they don’t follow from Euclid’s postulates. They follow the axioms.

** Answer: **

It is given that ** AC = BC **

Now,

In the figure given above, AB coincides with AC + BC.

Also, Euclid’s Axiom (4) says that things which coincide with one another are equal to one another. So, it can be deduced that AC + BC = AB

Now,

2AC = AB

Therefore,

** Hence proved. **

** Answer: **

Let's assume that there are two midpoints C and D

Now,

If C is the midpoint then, AC = BC

And

In the figure given above, AB coincides with AC + BC.

Also, Euclid’s Axiom (4) says that things which coincide with one another are equal to one another. So, it can be deduced that AC + BC = AB

From this, we can say that

2AC = AB -(i)

Similarly,

If D is the midpoint then, AD = BD

And

In the figure given above, AB coincides with AD + BD.

Also, Euclid’s Axiom (4) says that things which coincide with one another are equal to one another. So, it can be deduced that AD + BD = AB

From this, we can say that

2AD = AB -(ii)

Now,

From equation (i) and (ii) we will get

AD = AC

and this is only possible when C and D are the same points

Hence, our assumption is wrong and there is only one midpoint of line segment AB.

** Q6 ** In Fig. 5.10, if AC = BD, then prove that AB = CD.

** Answer: **

From the figure given in the problem,

We can say that

AC = AB + BC and BD = BC + CD

Now,

It is given that AC = BD

Therefore,

AB + BC = BC + CD

Now, According to Euclid's axiom, when equals are subtracted from equals, the remainders are also equal. Subtracting BC from both sides.

We will get

AB + BC - BC = BC + CD - BC

AB = CD ** Hence proved **

** Answer: **

** Axiom 5 ** states that the whole is greater than the part.

Lets take A = x + y + z

where A , x , y , z all are positive numbers

Now, we can clearly see that A > x , A > y , A > z

Hence, by this we can say that the whole (A) is greater than the parts. (x , y , z)

** Class 9 maths chapter 5 NCERT solutions Excercise: 5.2 **

** Q1 ** How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

** Answer: **

Euclid's postulate 5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Now, in an easy way

Let the line PQ in falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than 180° on the left side of PQ. Therefore, the lines AB and CD will eventually intersect on the left side of PQ.

** Q2 ** Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

** Answer: ** According to Euclid's 5 postulates, the line PQ falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than 180° on the left side of PQ. Therefore, the lines AB and CD will eventually intersect on the left side of the PQ

Now,

If then, the line never intersects with each other.

Therefore, we can say that lines AB and CD are parallel to each other

5.1 Introduction to Euclid’s Geometry

5.2 Euclid’s Definitions, Axioms, and Postulates

5.3 Equivalent Versions of Euclid’s Fifth Postulate

Interested students can study class 9 maths ch 5 question answer using the exercise solution links given below.

- Introduction To Euclid's Geometry Solutions Exercise 5.1
- Introduction To Euclid's Geometry Solutions Exercise 5.2

**Comprehensive Coverage:** NCERT solutions for maths chapter 5 class 9 typically provide in-depth coverage of the chapter's topics, ensuring that all key concepts and subtopics are addressed.

**Clear and Concise Explanations:** The solutions for ch 5 maths class 9 offer clear and concise explanations for complex scientific concepts, making it easier for students to understand.

**Step-by-Step Solutions:** Problems and exercises are accompanied by step-by-step solutions, aiding students in understanding the problem-solving process.

Chapter No. | Chapter Name |

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | |

Chapter 5 | Introduction to Euclid's Geometry |

Chapter 6 | |

Chapter 7 | |

Chapter 8 | |

Chapter 9 | |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 | |

Chapter 14 | |

Chapter 15 |

**How To Use NCERT Solutions For Class 9 Maths Chapter 5 **

- Go through each and every theorem and property have given at the start of the chapter.
- Have a glance through some examples given using those theorem and properties.
- Now, you can jump to the practice exercises to implement the acquired knowledge.
- During the practice, if you stuck anywhere then you can take the help of NCERT solutions for class 9 maths chapter 5 Introduction to Euclid's Geometry.
- Once you complete the above three points, then you can do some more practice using past papers.

1. Do NCERT class 9 maths chapter 5 solutions align well with the CBSE curriculum for students?

NCERT Solutions have long been recommended as a comprehensive learning resource for CBSE students to enhance their analytical skills. They have become an indispensable tool for comprehending the syllabus and building the confidence necessary to approach exams. The NCERT Solutions for Class 9 Maths Chapter 5 provide a precise explanation of the steps involved in solving a problem, covering all crucial aspects without skipping any essential details.

2. From which source can I obtain the solution for introduction to euclid's geometry Class 9 Maths Chapter 5?

Here NCERT solutions for class 9 maths students can find these solutions. Also, Careers360 website offers NCERT Solutions for Class 9 Maths Chapter 5, which are considered a crucial study material for Class 9 students. The solutions available on Careers360 are formulated meticulously, with every step explained in detail to provide clarity to the students. Our subject experts have prepared the solutions for Class 9 Maths NCERT to aid students in their board exam preparation. It is imperative for students to become well-versed in these solutions to obtain a good score in the Class 9 examination.

3. What is the meaning of Euclidean geometry according to NCERT Solutions for introduction to euclids geometry class 9?

The study of geometrical shapes and figures based on various axioms and theorems is known as Euclidean geometry. This type of geometry is primarily developed for two-dimensional, flat surfaces and is well-suited for explaining the shapes of geometrical figures and planes. Referring to NCERT Solutions for Class 9 Maths Chapter 5 can aid students in achieving a good score in their exams.

4. How does the NCERT solutions are helpful ?

NCERT solutions are provided in a very detailed manner which is helpful for the students if they stuck while solving NCERT problems. These solutions will give them conceptual clarity.

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