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CBSE Questions for Class 9 Maths Introduction To Euclid'S Geometry Quiz 1 - MCQExams.com
CBSE
Class 9 Maths
Introduction To Euclid'S Geometry
Quiz 1
Things which are three times of the same thing are
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equal to each other
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not equal to each other
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half of the same
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double of the same thing
Explanation
Let $$x=3a$$ and $$y=3a$$ when $$x,\ y$$ and $$a$$ are arbitrary numbers or things.
Then, by the first axiom of Euclid, $$x=y.$$
Two intersecting lines cannot be parallel to the same line is stated in the form of :
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an axiom
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a definition
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a postulate
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a proof
Explanation
Axiom
example if line A and line B are intersecting and line C is parallel to line A then line C is not parallel to line B.
$$A$$
Which Euclid's postulate led to the discovery of several other geometries while attempting to prove it using other postulates and axioms
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Fifth Postulate
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First Postulate
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Second Postulate
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Third Postulate
Explanation
Attempts to prove Euclid's Fifth Postulate using other postulates and axioms led to the discovery of several others geometries
Euclid stated that if equals are subtracted from equals, the remainders are equals in the form of :
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an axiom
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a postulate
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a definition
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a proof
Explanation
The above statement is Euclid's third axiom which states that
If equals are subtracted from equals, the remainders are equal.
So, $$A$$ is correct.
John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid's axiom that illustrates the relative ages of John and Ram.
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First axiom
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Second axiom
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Third axiom
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Fourth axiom
Explanation
Given that,
John's age $$=$$ Mohan's age &
Ram's age $$=$$
Mohan's age.
Euclid's first axiom states that,
things which are equal to the same thing, are equal to one another.
So, by the first axiom of Euclid,
John's age $$=$$ Ram's age.
Hence, Euclid's first axiom is applicable here.
Euclid's stated that all right angles are equal to each other in the form of :
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an axiom
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a definition
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a postulate
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a proof
Explanation
One of Euclid's five postulates is:
$$All$$ $$right$$ $$angles$$ $$are$$ $$CONGRUENT$$.
So, the correct option is $$C$$.
The things which are double of same thing are :
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equal
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halves of same thing
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unequal
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double of the same thing
Explanation
According to an Euclidian axiom,
The things which are double of the same things are equal to one another.
Example : if $$2x=2y,$$ then $$x=y$$.
Hence, option A is correct.
Euclid's fifth postulate is
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the whole is greater than the part
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a circle may be described with any centre and any radius
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all right angles are equal to one another
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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
Explanation
The fifth postulates of Euclid is
if a straight line, falling on two straight lines, makes the interior angles on the same side of it together less than two right angles, then the two strait lines, if produces indefinitely, meet on that side on which the sum of the angles is less than two right angles.
Ans- Option D.
Euclidean geometry is valid only for curved surfaces.
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True
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False
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Sometimes True
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Data Insufficient
Explanation
Euclid's postulates:
$$\Rightarrow$$ A straight line can be drawn joining any two points.
$$\Rightarrow$$ A straight line segment can be extended indefinitely in a straight line.
$$\Rightarrow$$ A circle can be drawn having the segment as radius and one endpoint as center.
$$\Rightarrow$$ All right angles are congruent and equal.
$$\Rightarrow$$ Parallel postulate.
Hence, we can observe that euclidian geometry is valid for 2-dimensional geometrical figures.
Axioms are assumed
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universal truths in all branches of mathematics
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universal truths specific to geometry
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theorems
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definitions
Explanation
From time immemorial, axioms have been acquired by man through the day to day experiences.
No mathematical deduction is needed to prove them.
Practically they are starting points of reasoning.
So axioms are assumed universal truths in all branches of mathematics.
Ans- Option A.
The things which coincide with one another are:
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equal to another
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unequal
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double of same thing
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Triple of same things
Explanation
According to Euclid's postulates, $$\text{equal}$$ things coincide with each other.
Hence, $$A$$ is correct.
The boundaries of the solids are called curves.
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True
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False
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Ambiguous
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Data Insufficient
Explanation
The boundaries of the solids are called surfaces.
While the boundaries of the surfaces are called curves.
According to Euclid :
The whole is greater than the part .State whether that this is true or false.
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True
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False
Explanation
Consider the three numbers $$A,\ B$$
A,B
and $$C$$
C
Let us consider,
$$\Rightarrow C=A+B$$ $$...(1)$$
For example, $$A=4$$ and $$B=6$$ $$...(2)$$
From equation $$(1)$$
$$\Rightarrow C=4+6$$
Therefore, $$C=10$$ $$...(3)$$
(3)
Hence, from equation $$(3),$$
(3)
it is seen that the sum that $$C=10$$
C=10
is greater that both the number that is $$A$$
and $$B$$
B
that is $$4$$
4
and $$6$$
respectively.
Therefore, the whole is greater than the part
Hence the given statement is true.
The total number of propositions in the Elements book written by Euclid are
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$$465$$
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$$460$$
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$$13$$
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$$55$$
Explanation
Elements is the book written by a mathematician Euclid's and it has $$465$$ propositions , $$131$$ definitions $$5$$ postulates of Euclid's and $$5$$ common notions are written
Therefore, there are $$465$$ propositions in the elements.
It is known that $$x+y=10,$$ then $$x+y+z=10+z$$. The Euclid's axiom that illustrates this statement is
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First axiom
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Second axiom
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Third axiom
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Fourth axiom
Explanation
Here $$z$$ has been added to two quantities that are equal.
So, by Euclid's second axiom, which states that, If equals are added to equals then wholes are equal,
$$\Rightarrow x+y+z=10+z$$
Hence, $$x+y+z=10+z$$ is true by the second axiom of Euclid.
Euclid belonged to which of the following country?
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Babylonia
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Egypt
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Greece
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India
Explanation
Euclid belonged to Greece.
Ans- Option C.
Euclid's fourth axiom says that everything equals itself.
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True
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False
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Ambiguous
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Data insufficient
Explanation
Euclid's fourth axiom states that "things which coincide with one another are equal to one another." In other words, "everything equals itself."
Hence, the given statement is true.
$$\angle A=\angle B$$ and $$\angle B=\angle C$$, According to which axiom of Euclid the relation between $$\angle A$$ and $$\angle C$$ is established?
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I
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II
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III
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IV
Explanation
Given that $$\quad \angle A=\angle B\quad \& \quad \angle B=\angle C.\quad $$
Then, according to Euclid's first axiom, which states that
"Things which are equal to the same thing are also equal to each other".
Therefore,
$$\quad \angle A=\angle C\quad $$
Ans- Option A.
The Euclidean geometry is valid only for figures in the plane.
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True
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False
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Ambiguous
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Data Insufficient
Explanation
The given statement is true. Because,
by Einstein's theory of
general
relativity, physical space itself is not Euclidean. Euclidean space is a good approximation for it where the gravitational field is weak.
So, in space or in multidimensional space the Euclidean axioms are not applicable.
Ans- Option A.
Euclid stated that all right angles are equal to each other in the form of
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an axiom
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a definition
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a postulate
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a proof
Explanation
Euclid's fourth Postulate states that all right angles are equal to each other.
Ans- Option C.
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