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NCERT exemplar Class 9 Maths solutions chapter 5 provide students with detailed answers for chapter 5- Introduction to Euclid’s Geometry. Euclidean geometry was developed by Alexandrian Greek mathematician Euclid. The chapter deals with the fundamentals of Euclidean Geometry which helps the student to understand the space around us. A team of subject experts created these NCERT exemplar solutions for Class 9 Maths chapter 5. These NCERT Solutions help in understanding Euclid's Geometry concepts in a better and easier way. The NCERT exemplar Class 9 Maths chapter 5 solutions is in accord with the CBSE Syllabus for Class 9 Maths.
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Question:1
The three steps from solids to points are:
(A) Solids - surfaces - lines - points
(B) Solids - lines - surfaces - points
(C) Lines - points - surfaces - solids
(D) Lines - surfaces - points - solids
Answer:
(A) Solids - surfaces - lines - pointsQuestion:2
The number of dimensions, a solid has:
(A) 1
(B) 2
(C) 3
(D) 0
Answer:
(C) 3Question:3
The number of dimensions, a surface has:
(A) 1
(B) 2
(C) 3
(D) 0
Answer:
(B) 2Question:4
The number of dimension, a point has:
(A) 0
(B) 1
(C) 2
(D) 3
Answer:
(A) 0Question:5
Euclid divided his famous treatise “The Elements” into:
(A) 13 chapters
(B) 12 chapters
(C) 11 chapters
(D) 9 chapters
Answer:
(A) 13 chaptersQuestion:6
The total number of propositions in the Elements are:
(A) 465
(B) 460
(C) 13
(D) 55
Answer:
Answer:(A) 465Question:7
Boundaries of solids are:
(A) surfaces
(B) curves
(C) lines
(D) points
Answer:
(A) surfacesQuestion:8
Boundaries of surfaces are:
(A) Surfaces
(B) curves
(C) lines
(D) points
Answer:
(B) curvesQuestion:9
In Indus Valley Civilization (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio
(A) 1 : 3 : 4
(B) 4 : 2 : 1
(C) 4 : 4 : 1
(D) 4 : 3 : 2
Answer:
(B) 4 : 2 : 1Question:10
A pyramid is a solid figure, the base of which is
(A) only a triangle
(B) only a square
(C) only a rectangle
(D) any polygon
Answer:
Answer:Question:11
The side faces of a pyramid are:
(A) Triangles
(B) Squares
(C) Polygons
(D) Trapeziums
Answer:
(A) TrianglesQuestion:12
(A) First Axiom
(B) Second Axiom
(C) Third Axiom
(D) Fourth Axiom
Answer:
(B) Second AxiomQuestion:13
In ancient India, the shapes of altars used for household rituals were:
(A) Squares and circles
(B) Triangles and rectangles
(C) Trapeziums and pyramids
(D) Rectangles and squares
Answer:
(A) Squares and circlesQuestion:14
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:
(A) Seven
(B) Eight
(C) Nine
(D) Eleven
Answer:
Answer:(C) NineQuestion:15
Greeks emphasized on:
(A) Inductive reasoning
(B) Deductive reasoning
(C) Both A and B
(D) Practical use of geometry
Answer:
Answer:(B) Deductive reasoningQuestion:16
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for:
(A) Public worship
(B) Household rituals
(C) Both A and B
(D) None of A, B, C
Answer:
(A) Public worshipQuestion:17
Euclid belongs to the country:
(A) Babylonia
(B) Egypt
(C) Greece
(D) India
Answer:
(C) GreeceQuestion:18
Thales belongs to the country:
(A) Babylonia
(B) Egypt
(C) Greece
(D) Rome
Answer:
(C) GreeceQuestion:19
Pythagoras was a student of:
(A) Thales
(B) Euclid
(C) Both A and B
(D) Archimedes
Answer:
(A) ThalesQuestion:20
Which of the following needs a proof?
(A) Theorem
(B) Axiom
(C) Definition
(D) Postulate
Answer:
(A) TheoremQuestion:21
Euclid stated that all right angles are equal to each other in the form of
(A) an axiom
(B) a definition
(C) a postulate
(D) a proof
Answer:
(C) a postulateQuestion:22
‘Lines are parallel if they do not intersect’ is stated in the form of
(A) an axiom
(B) a definition
(C) a postulate
(D) a proof
Answer:
Answer:Question:1
Answer:
FalseQuestion:2
Answer:
FalseQuestion:3
Answer:
FalseQuestion:4
Answer:
TrueQuestion:5
Answer:
TrueQuestion:6
Answer:
FalseQuestion:7
Answer:
TrueQuestion:8
Answer:
TrueQuestion:9
Answer:
TrueQuestion:1
Answer:
Sales in September are also equal.Question:2
Answer:
Euclid’s axiom According to Euclid’s axiom, if equals are added to equals, the wholes are equal.Question:3
Answer:
To prove: AH > Sum of lengths of AB + BC + CDQuestion:4
Answer:
To prove: AX = CYQuestion:5
Answer:
Solution:Question:6
Answer:
Solution:Question:7
Answer:
To Prove: 1 = 3Question:8
Answer:
To prove: A = CQuestion:9
Answer:
Solution:Question:11
Answer:
Given that:Question:12
i) Solve each of the following question using appropriate Euclid’s axiom: In the Fig. 5.12:
AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC.
ii) Solve each of the following question using appropriate Euclid’s axiom: In the Fig. 5.12:
BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
Answer:
i) Here AB = BCQuestion:1
Answer:
Defined terms are:Question:2
Answer:
Euclid’s fifth postulate: if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.Question:3
Read the following statements which are taken as axioms:
Answer:
Given the system of axioms is not consistent.Question:4
Read the following two statements which are taken as axioms:
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to 180°.
Is this system of axioms consistent? Justify your answer.
Answer:
Given system of axioms is not consistent.Question:5
Answer:
Given the system of axioms is consistent.Topics covered in NCERT exemplar Class 9 Maths solutions chapter 5 deals with the understanding of:
◊ Definitions of solids planes lines and points.
◊ Euclid gives some important axioms in his textbook "element".
◊ NCERT exemplar Class 9 Maths solutions chapter 5 deal with problems based on Euclid's five postulates described in his textbook element.
◊ The fifth axiom about parallel postulate was very useful but not intuitive; therefore, many other logical equivalent postulates are given.
◊ Two of them are discussed in this chapter.
These Class 9 Maths NCERT exemplar chapter 5 solutions will help understand the elements described by Euclid as a small set of axioms and prove some theorems based on them. The axioms of Euclidean geometry are intuitive and help to derive theorems which are deductive and logical. It defines the Euclidean space and gives three dimensions and is very useful for students to understand and differentiate between plane solids and various structures. The Class 9 Maths NCERT exemplar solutions chapter 5 Introduction to Euclid’s Geometry will be useful to built a basics in the chapter and to solve problems in reference books such as NCERT Class 9 Maths, RD Sharma Class 9 Maths, RS Aggarwal Class 9 Maths etcetera.
NCERT exemplar Class 9 Maths solutions chapter 5 pdf download can also be utilised by the students. Users can download the solutions using any online tools available to convert web pages to pdf.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
Yes, there are three types of geometries known as Euclidean geometry, spherical geometry and hyperbolic geometry. They try to deal with two-dimensional space.
Einstein is not directly associated with Euclidean Geometry. In early 1900, Einstein proved that Euclidean space is not the same as Euclidean space described by Euclid.
It is not directly used; however, it gives a student the basics to understand the structures, many theorems and fundamentals of physics, and mathematics.
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