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CBSE Questions for Class 9 Maths Introduction To Euclid'S Geometry Quiz 4 - MCQExams.com
CBSE
Class 9 Maths
Introduction To Euclid'S Geometry
Quiz 4
Write whether the following statements are True or False? Justify your answer:
Two distinct intersecting lines cannot be parallel to the same line.
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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 figure A and B are the centres of the two intersecting circles.
With the help of Euclid's first axiom, state the type of $$\Delta ABC$$.
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An equilateral triangle.
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An isosceles triangle
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A scalene triangle
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A right angle triangle
Explanation
From the above figure, $$AB$$ and $$AC$$ are the radii of the circle on the left, where $$C$$ is the point of intersection of the two circles.
Similarly, $$BA$$ and $$BC$$ are the radii of the circle on the right, where $$C$$ is the point of intersection of the two circles.
We know, $$AB = AC$$ and $$BC = AB,$$ thus by Euclid's first axiom, $$AC = BC.$$
Hence $$AC = BC = AB$$ which makes triangle $$ABC$$ an equilateral triangle.
Select the correct match.
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Postulate III $$\quad$$ A terminated line can be produced indefinitely
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Postulate II $$\quad$$ All right angles are equal to one another
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Postulate IV $$\quad$$ A circle can be drawn with any centre and any radius
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Postulate I $$\quad$$ A straight line may be drawn from any one point to any other point.
Explanation
Postulates
1. A straight line may be drawn from any point to any other point.
2. A terminated line (line segment) can be produced indefinitely.
3. A circle may be described with any centre and any radius.
4. All right angles are equal to one another.
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
So, (D) option is correct.
Answer (D)
Postulate I
A straight line may be drawn from any one point to any other point.
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
Postulate says, if a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles
many tried to prove it but at the end they had to assume something which was very closely related to the fifth postulate, they didnot form any new geometries but from where they started they ended at the same point.
$$B$$
State the Euclid's axiom used in the following statements
$$AD < AB$$
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Axiom 5
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Axiom 1
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Axiom 3
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Axiom 2
Does Euclid' fifth postulate imply the existence of parallel lines? Explain
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True
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False
Explanation
Yes, Euclid's fifth postulate is valid for parallelism of lines because, if a straight line $$l$$ falls on two straight lines $$m$$ and $$n$$ such that sum of the interior angles on one side of $$l$$ is two right angles, then by Euclid's fifth postulate the line will not meet on this side of $$l$$.
Next, you know that the sum of the interior angles on the other side of line $$l$$ will also be two right angles.
Therefore, they will not meet on the other side also. So, the lines $$m$$ and $$n$$ never meet and are, therefore, parallel.
Read the following axioms:
(i) Things which are equal to the same thing are equal to one another.
(ii) If equals are added to equals, the wholes are equal.
(iii) Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.
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Consistent
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Inconsistent
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Either
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Neither
Explanation
This set of axiom is consistent.
(i) If a=b and b=c then a =c
(ii) If a = b and c = d then a+ b =c +d
(iii) If x = 2y and z = 2y then x = z
Two distinct ________ lines cannot be parallel to the same line.
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Intersecting
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Non-intersecting
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Parallel
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None of these
Explanation
Two intersecting lines cannot be parallel to same line as this statement is equivalent to
Euclid's fifth postulate.
Euclid's second axiom is
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the things which are equal to the same thing are equal to one another
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if equals be added to equals, the wholes are equal
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if equals be subtracted from equals, the remainders are equals
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things which coincide with one another are equal to one another
Explanation
Euclid's second axiom can be stated as any terminated straight line can be projected indefinitely or it can be stated as if equals be added to equals, the wholes are equal.
Euclid stated that all right angles are equal to one another in the form of a/an ..........
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Axiom
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Defination
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Postulate
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Proof
Explanation
Postulates
1. A straight line may be drawn from any point to any other point.
2. A terminated line (line segment) can be produced indefinitely.
3. A circle may be described with any centre and any radius.
4. All right angles are equal to one another.
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 the two straight lines if
produced indefinitely, meet on that side on which the sum of angles is taken together
less than two right angles.
Euclid used the term postulate for the assumptions that were specific to geometry
and otherwise called axioms. A theorem is a mathematical statement whose truth
has been logically established.
Answer (C)
Postulate
_______ is another name for postulate.
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theorem
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conjectures
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axiom
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operation
Explanation
A postulate is a statement that is accepted without proof. Axiom is another name for a postulate.
For example, if you know that Pam is five feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings are at least five foot one. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.
It is possible to draw a straight line from any point to any other point. The given statement is _________.
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theroem
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conjectures
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postulate
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operation
Explanation
It is possible to draw a straight line from any point to any other point.
A postulate is a statement that is accepted without proof. Axiom is another name for a postulate.
For example, if you know that Pam is five feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings are at least five foot one. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.
Identify the given statement: A circle can be described with any given center and radius.
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postulate
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conjectures
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theorem
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operation
Explanation
A circle can be described with any given center and radius.
The given statement is postulate. A postulate is a statement that is accepted without proof. Axiom is another name for a postulate.
For example, if you know that Pam is five feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings are at least five foot one. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.
Which of the following is NOT a Euclid's postulate?
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We can describe a circle with any center and radius
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All right angles are equal to one another
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There is a unique line that passes through two given points
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Through a point not on a given line, exactly one parallel line may be drawn to the given line
Explanation
Following statement is not a Euclid's postulate:-
Through a point not on a given line, exactly one parallel line may be drawn to the given line.
_____is regarded as the Father of Geometry.
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Thales
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Pythagoras
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Gauss
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Brahmgupta
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Euclid
A statement accepted as true as the basis for argument or inference, is
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Axioms
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Conjecture
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Corollary
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Theorem
Explanation
A statement accepted as true as the basis for argument or inference, is axioms.
Let us consider an axiom of addition and multiplication.
Let $$x$$ and $$y$$ be real numbers.
Then $$x + y$$ is also a real number and $$xy$$ is also a real number.
Euclidian geometry cannot be applied to which of the following?
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Triangle
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Rectangle
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Sphere
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Square
Explanation
Euclidian Geometry can not be applied to Sphere as it is a 3-dimensional object.
In connection with proof in geometry, indicate which one of the following statements is incorrect:
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Some statements are accepted without being proved.
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In some instances there is more than one correct order in proving certain propositions.
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Every term used in a proof must have been defined previously.
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It is not possible to arrive by correct reasoning as a true conclusion if, in the given, there is an untrue proposition.
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Indirect proof can be used whenever there are two or more contrary propositions.
Explanation
is incorrect since some terms (primitives) must necessarily remain undefined.
Write whether the following statements are True or False? Justify your answer:
If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.
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True
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False
Choose the correct option
If a = 6 and b = a, then b = 60 by
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Axiom 1
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Axiom 2
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Axiom 3
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Axiom 4
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