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CBSE Questions for Class 9 Maths Introduction To Euclid'S Geometry Quiz 3 - MCQExams.com
CBSE
Class 9 Maths
Introduction To Euclid'S Geometry
Quiz 3
___________ was the most logical and abstract creator of Euclid's geometry approach.
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Hilbert
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Bhasharacharya
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Thelus
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Pythagoras
Explanation
Pythagoras developed the theory of geometry to a great extent.
Thus Pythagoras was the most logical and abstract creator of Euclid's geometry approach.
According to Euclid's axioms, the _____ is greater than the part.
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Half
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Large
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Whole
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None of these
Explanation
According to an axiom of Euclid, whole is greater than the part and it is a universal truth.
Things which are halves of the _____ things are equal to one another.
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Same
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Different
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Two
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None of these
Explanation
According to the first Euclid's axioms ''
Things which are equal to the same thing are equal to one another''.
In this case, If t
hings which are halves of the same things then, they are equal to one another.
If point $$P$$ lies on $$AB$$, then $$AB$$ is always greater than $$AP$$. This concept is on which of the following Euclid's Axioms.
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First Axiom
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Second Axiom
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Third Axoim
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Fifth Axiom
Explanation
The fifth axiom of Euclid's about geometry is the whole of anything is greater than the part of it.
Here AB is the whole line and AP is the part and according to the fifth axiom we have AB is always greater than AP.
So the given statement is Euclid's fifth axiom.
In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio
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1 : 3 : 4
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4 : 2 : 1
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4 : 4 : 1
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4 : 3 : 2
Explanation
Bricks used for construction work were having dimensions in the ratio are 4 : 2 : 1.
Hence. (b) is the correct answer.
Which of the following is Euclid's first postulate?
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All right angles are equal to one another.
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The whole is greater then the part.
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A circle can be drawn with any centre and any radius.
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A straight line segment can be drawn joining any two points.
Explanation
Euclid's first postulate is :
A straight line segment can be drawn joining any two points.
Thus, option D is correct.
The total number of propositions in the Elements are:
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465
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460
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13
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55
Explanation
The total number of propositions in the Elements are 465.
Note: The statements that can be proved are called propositions or theorems. Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems.
Hence. (a) is the correct answer.
The three steps from solids to points are:
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Solids - surfaces - lines points
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Solids - lines - surfaces - points
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Lines points surfaces solids
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Lines - surfaces - points solids
Explanation
The three steps from solids to points are solids•surface•lines-points.
Hence. (a) is the correct answer.
Euclid divided his famous treatise The Elements" into:
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13 chapters
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12 chapters
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11 chapters
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9 chapters
Explanation
Euclid divided his famous treatise 'The Elements" into 13 chapters.
Hence, (a) is the correct answer.
It is known that if $$x + y = 10$$ 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
If $$x + y = 10$$ then $$x + y + z = 10 + z$$. The Euclid's axiom that illustrates this statement Is axiom 2 which states that; if equals are added to equals, the wholes are equal.
Hence, (b) is the correct answer.
The number of dimensions, a surface has:
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1
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2
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3
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0
Explanation
A surface has 2 dimensions.
Hence, (b) is the correct answer.
Write whether the following statement is True or False? Justify your answer:
The things which are double the same thing are equal to one another.
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True
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False
Explanation
True
Since it is one of Euclid's axioms. Some of Euclid's axioms are:
(1) Things which are equal to the same thing are equal to one another.
(2) If equals are added to equals, the wholes are equal
(3) If equals are subtracted from equals, the remainder are equal.
(4) Things which coincide with one another are equal to one another.
(5) The whole is greater than the part.
(6) Things which are double of the same things are equal to one another.
(7) Things that are halves of the same things are equal to one another.
Write whether the following statements are True or False? Justify your answer:
'For every line 1 and for every point P not lying on a given linethere exists a unique line m passing through P and parallel to 1" is known as Playfair's axiom.
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True
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False
Explanation
The given statement is true, because it is an equivalent version of Euclid's fifth postulate.
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for:
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Public worship
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Household rituals
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Both A and B
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None of A, B, C
Explanation
In Ancient India, Altars with combination of shapes like rectangles. triangles and trapeziums were used for public worship.
Hence. (a) is the correct answer.
The number of interwoven isosceles triangles in Sriyantra (in the Atharva Veda) is:
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Seven
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Eight
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Nine
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Eleven
Explanation
The number of interwoven isosceles triangle in Sriyantra (in the Atharva Veda) is nine.
Hence, (c) is the correct answer.
Euclid belongs to the country:
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Babylonia
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Egypt
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Greece
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India
Explanation
Euclid belongs to the country Greece. Euclid around 300 B.C. collected all known work in the field of mathematics and arranged it in his famous treatise called Elements.
Hence, (c) is the correct answer.
Write whether the following statements are True or False? Justify your answer:
The boundaries of the solids are curves.
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True
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False
Explanation
The given statement is false because boundaries of solids are surfaces.
Write whether the following statements are True or False? Justify your answer:
The statements that are proved are called axioms.
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True
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False
Explanation
The given statement is false because the statement that are proved are called theorems.
Write whether the following statements are True or False? Justify your answer:
Euclidean geometry is valid only for curved surfaces.
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True
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False
Explanation
The given statement is false because Euclidean geometry is valid only for the figures in the plane.
State true or false:
Attempts to prove Euclid's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
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True
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False
Explanation
Attempts to prove Euclid's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
It is a great achievement in the creation of several other geometries. These geometries are quite different from Euclidean geometry and are called non-Euclidean geometry.
Hence, the given statement is $$True$$.
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