R.d Sharma 2022 Mcqs Solutions for Class 9 Maths Chapter 9 Introduction To Euclid's Geometry are provided here with simple step-by-step explanations. These solutions for Introduction To Euclid's Geometry are extremely popular among class 9 students for Maths Introduction To Euclid's Geometry Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the R.d Sharma 2022 Mcqs Book of class 9 Maths Chapter 9 are provided here for you for free. You will also love the ad-free experience on Meritnation’s R.d Sharma 2022 Mcqs Solutions. All R.d Sharma 2022 Mcqs Solutions for class 9 Maths are prepared by experts and are 100% accurate.
Page No 90:
Question 1:
Euclid belongs to the country
(a) Babylonia
(b) Egypt
(c) Greece
(d) Rome
Answer:
Euclid belongs to the country Greece.
Hence, the correct answer is option (c).
Page No 90:
Question 2:
Thales belongs to the country
(a) Babylonia
(b) Egypt
(c) Greece
(d) Rome
Answer:
Thales belongs to the country Greece.
Hence, the correct answer is option (c).
Page No 90:
Question 3:
Pythagoras was a student of
(a) Thales
(b) Euclid
(c) Both (a) and (b)
(d) Archimedes
Answer:
Pythagoras was a student of Thales.
Hence, the correct answer is option (a).
Page No 90:
Question 4:
Which of the following needs a proof?
(a) Theorem
(b) Axiom
(a) Definition
(d) Postulate
Answer:
Theorem needs a proof. Theorems are statements which are proved using definitions, axioms, previously proved statements and deductive reasoning.
Hence, the correct answer is option (a).
Page No 90:
Question 5:
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:
Euclid stated that all right angles are equal to each other in the form of a postulate. Euclid's postulate 4 states that all right angles are equal to one another.
Hence, the correct answer is option (c).
Page No 90:
Question 6:
'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:
'Lines are parallel if they do not intersect' is stated in the form of a definition. Definition of parallel lines is lines are parallel if they do not intersect.
Hence, the correct answer is option (b).
Page No 90:
Question 7:
Euclid's second axiom is
(a) The things which are equal to the same thing are equal to one another.
(b) If equals be added to equals, the wholes are equal.
(c) If equals be subtracted from equals, the remainders are equals.
(d) Things which coincide with one another are equal to one another.
Answer:
Euclid's second axiom is "if equals be added to the equals, the wholes are equal".
Hence, the correct answer is option (b).
Page No 90:
Question 8:
Euclid's fifth postulate is
(a) The whole is greater than the part.
(b) A circle may be described with any centre and any radius.
(c) All right angles are equal to one another.
(d) 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 the angles is less than two right angles.
Answer:
Euclid's fifth postulate is "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 the angles is less than two right angles."
Hence, the correct answer is option (d).
Page No 90:
Question 9:
Things which are double of the same thing are
(a) equal
(b) unequal
(c) halves of the same thing
(d) double of the same thing
Answer:
According to Euclid's 6th Axiom "Things which are double of the same thing are equal".
Hence, the correct answer is option (a).
Page No 90:
Question 10:
Axioms are assumed
(a) universal truths in all branches of mathematics
(b) universal truths specific to geometry
(c) theorems
(d) defintitions
Answer:
Axioms are assumed to be universal truths in all branches of mathematics.
Hence, the correct answer is option (a).
Page No 90:
Question 11:
If a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is 120º, then the two straight lines, if produced indefinitely, meet on the side on which the sum of the angles is
(a) less than 120º
(b) greater than 120º
(c) is equal to 120º
(d) greater than 180º
Answer:
Euclid's fifth postulate is "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 the angles is less than two right angles."
So, if a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is 120º, then the two straight lines, if produced indefinitely, meet on the side on which the sum of the angles is equal to 120º.
Hence, the correct answer is option (c).
Page No 90:
Question 12:
Greek's emphasised on:
(a) inductive reasoning
(b) deductive reasoning
(c) both (a) and (b)
(d) practical use of geometry
Answer:
Greek's emphasised on deductive reasoning.
Hence, the correct answer is option (b).
Page No 90:
Question 13:
Euclid divided his famous treatise "The Elements" into:
(a) 13 chapters
(b) 12 chapters
(c) 11 chapters
(d) 9 chapters
Answer:
Euclid divided his famous treatise "The Elements" into 13 chapters.
1. Triangles, parallels, and area
2. Geometric algebra
3. Circles
4. Constructions for inscribed and circumscribed figures
5. Theory of proportions
6. Similar figures and proportions
7. Fundamentals of number theory
8. Continued proportions in number theory
9. Number theory
10. Classification of incommensurables
11. Solid geometry
12. Measurement of figures
13. Regular solids
Hence, the correct answer is option (a).
Page No 90:
Question 14:
The total number of propositions in "The Elements" are
(a) 465
(b) 460
(c) 13
(d) 55
Answer:
Euclid deduced 465 propositions in a logical chain making use of his definitions, postulates, axioms and theorems. Therefore, the total number of propositions is 465.
Hence, the correct answer is option (a).
Page No 90:
Question 15:
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:
(a) 7
(b) 8
(c) 9
(d) 11
Answer:
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is 9.
Hence, the correct answer is option (c).
Page No 91:
Question 16:
In ancient India, the shapes of altras used for house hold rituals were:
(a) squares and circles
(b) triangles are rectangles
(c) trapezium and pyramids
(d) rectangles and squares
Answer:
Altars and fireplaces were created for doing many rituals and for the worship of God. The concept of geometry came from the construction of these altars and fireplaces. These altars were used for sacrifices and the people followed the instructions written in sulbasutras for proper positioning of the altars and fireplaces.
For household rituals, the altars and fireplaces used for worshipping were in the shape of squares and circles.
Hence, the correct answer is option (a).
Page No 91:
Question 17:
In ancient India, Altras 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:
Altars and fireplaces were created for doing many rituals and for the worship of God. The concept of geometry came from the construction of these altars and fireplaces.
These altars were used for sacrifices and the people followed the instructions written in sulbasutras for proper positioning of the altars and fireplaces.
For communal/public rituals, the altars and fireplaces used for worshipping were the combinations of various geometric shapes like rectangles, triangles, and trapezium.
Hence, the correct answer is option (a).
Page No 91:
Question 18:
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:
The steps from solids to point are solids-surfaces-lines-points.
Hence, the correct answer is option (a).
Page No 91:
Question 19:
The number of dimensions, a solid has
(a) 1
(b) 2
(c) 3
(d) 0
Answer:
A solid shape has shape, size, position and can be moved from one place to another. So, solid has three dimensions.
Hence, the correct answer is option (c).
Page No 91:
Question 20:
The number of dimensions, a surface has
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
Boundaries of a solid are called surfaces. A surface(plane) has only length and breadth. So, it has two dimensions.
Hence, the correct answer is option (c).
Page No 91:
Question 21:
The number of dimensions, a point has
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension.
Hence, the correct answer is option (a).
Page No 91:
Question 22:
Boundaries of solids are:
(a) surfaces
(b) curves
(c) lines
(d) points
Answer:
The boundaries of solids are surfaces.
Hence, the correct answer is option (a).
Page No 91:
Question 23:
Boundaries of surfaces are:
(a) surfaces
(b) curves
(c) lines
(d) points
Answer:
The boundaries of surfaces are curves.
Hence, the correct answer is option (b).
Page No 91:
Question 24:
In Indus Valley Civilisation (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:
In Indus valley civilization, the bricks used for construction work were having dimensions in the ratio 4 : 2 : 1.
Hence, the correct answer is option (b).
Page No 91:
Question 25:
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:
A pyramid is solid figure, the base of which is a triangle or square or some other polygon.
Hence, the correct answer is option (d).
Page No 91:
Question 26:
The side faces of pyramid are:
(a) triangles
(b) squares
(c) polygons
(d) trapeziums
Answer:
The side faces of a pyramid are always triangles.
Hence, the correct answer is option (a).
Page No 91:
Question 27:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): Euclidean geometry is valid only for curved surfaces.
Statement-2 (Reason): The things which are double of the same thing are equal to one another.
Answer:
Euclidean geometry is valid only for the figures in the plane but on curved surfaces, it fails.
Thus, ​Statement-1 is false.
One of Euclid’s axiom states that "The things which are double of the same thing are equal to one another".
Thus, Statement-2 is true.
So, Statement-1 is false, Statement-2 is true.
Hence, the correct answer is option (d).
Page No 91:
Question 28:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): Self-evident true statements are called axioms.
Statement-2 (Reason): Statements whose truth can be logically established are called theorems.
Answer:
Axioms are statements that are self-evident and are accepted without any proof.
Thus, Statement-1 is true.
A mathematical statement whose truth has been established (proved) is called a theorem.
Thus, Statement-2 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Hence, the correct answer is option (b).
Page No 91:
Question 29:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): The boundaries of the solids are surfaces.
Statement-2 (Reason): The boundaries of surfaces are lines.
Answer:
Boundaries of solids are known as surfaces.
Thus, Statement-1 is true.
Boundaries of surfaces are known as curves.
Thus, Statement-2 is false.
So, Statement-1 is true, Statement-2 is false.
Hence, the correct answer is option (c).
Page No 91:
Question 30:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): Everything equal to itself.
Statement-2 (Reason): Things which coincide with one another are equal to one another.
Answer:
Euclid’s fourth axiom says that everything equals itself. Which is the justification of the principle of superposition.
Thus, Statement-1 is true.
Using the principle of superposition, "things which coincide with one another are equal to one another".
Thus, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Hence, the correct answer is option (a).
Page No 91:
Question 31:
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): In geometry, we take a point, a line and a plane as undefined terms.
Statement-2 (Reason): Euclidean geometry is valid only for curved surfaces.
Answer:
To define a point, a line and a plane in geometry we need to define many other things that give a long chain of definitions without an end. For such reasons, mathematicians agree to leave these geometric terms undefined.
Thus, Statement-1 is true.
Euclidean geometry is based on the postulates and axioms that are valid for plane surfaces.
Euclidean is not physical space whereas curved space needs physical space.
So, it is not valid for curved surfaces.
Thus, Statement-2 is false.
So, Statement-1 is true, Statement-2 is false.
Hence, the correct answer is option (c).
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