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CBSE Questions for Class 9 Maths Introduction To Euclid'S Geometry Quiz 2 - MCQExams.com
CBSE
Class 9 Maths
Introduction To Euclid'S Geometry
Quiz 2
State the Euclid's axiom used in the following statements
$$\angle ACB > \angle DCB$$
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Axiom 5
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Axiom 2
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Axiom 4
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Axiom 3
Explanation
$$\angle ACB > \angle DCB$$
here axiom 5 is used which states that "the whole is greater than the part"
here we clearly see that $$\angle ACB$$ is greater than
$$\angle DCB$$
.
Two salesmen make equal sales during the month of August. In September, each salesman doubles his/her sale of the month of August. Compare their sales in September.
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Equal sales in September
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Unequal sales in September
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Ambiguous
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None of the above
Explanation
Let each salesman makes the sale of Rs. $$x$$ in August.
As per the question, In September, the sale of each salesman is Rs. $$2x$$.
According to Euclids sixth axiom, things that are double the same thing are equal to one another.
So, the sales of each salesman are equal in the month of september
Study the following statement:
"Two intersecting lines cannot be perpendicular to the same line".
Check whether it is an equivalent version to the Euclid's fifth postulate.
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True
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False
Explanation
According to
Euclid's fifth postulate
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.
Our statement is:
"Two intersecting lines cannot be perpendicular to the same line".
So from the fifth postulate that if two lines meet on third line
As one side on which the sum of angles is less than two right angles
As here two intersecting lines $$m$$ and $$n$$ are not perpendicular on line l
$$x + y >180^{\circ}$$
that means lines are not perpendicular to third line as their sum is less than two right angles.
So we can say that given statement is equivalent to Euclid's fifth postulate.
The edges of a surface 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 edges of a surface are called curves.
For example, circle is a plane surface and its edge is the circumference, which is a curve
The things which are double of the same thing are equal to one another.
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True
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False
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Ambiguous
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Data Insufficient
Explanation
Let $$a=2x$$ and $$b=2x$$ when $$a, b$$ & $$x$$ are arbitrary numbers or things.
The first axiom of Euclid states that :
"Things which are equal to the same thing are also equal to each other."
So $$a=b=2x$$
i.e the given statement is true.
Ans - Option A.
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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Only (i) & (ii) are consistent
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Only (iii) is consistent
Explanation
(i) This statement is Euclid's first Axiom.
(ii)
This statement is Euclid's Second Axiom.
(ii)
This statement is true if we apply Euclid's first Axiom.
Let $$2a=b$$ and $$2a=c$$.
then both $$b ~\&~ c$$ are equal to $$2a$$
i.e $$ b=c$$
which is consistent with the First Axiom of Euclid.
So the given system of axioms is consistent.
ans- Option A.
If equals are added to equals, then the wholes are .......
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unequal
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equal
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sometimes equal sometimes unequal
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nearest to each other
Explanation
According to the first axiom of Euclid " if equals are added to equals the wholes are equal."
Ans- Option B.
State true or false:
The statements that are proved, are called axioms.
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True
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False
Explanation
Axioms are statements which are self evident and are accepted without any proof.
But there are some statements which require proof and experimental verification to establish themselves. This type of statement is called a theory.
so the given statement is false.
Ans- Option B.
State TRUE or FALSE
Given any two distinct points A and B, there exists a third point C which is between A and B.
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True
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False
Explanation
Given any two distinct points A and B, there always exists a third point C which is between A and B.
And the point C may or may not lie on the line joining A and B.
A ______ is a statement that is accepted without proof.
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theorem
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conjectures
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postulate
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operation
Explanation
A postulate is a statement that is accepted without proof.
Example: A unique straight line can be drawn from any point to any other point.
If $$a=60$$ 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 $$4$$
Explanation
According to Euclid's 1st axiom,-
Things which are equal to the same thing are also equal to one another
So, if $$a=60$$ and $$b=a$$, then $$b=60$$ by $$Axiom1$$
Identify the given statement: It is possible to produce a finite straight continuously in a straight line.
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theroem
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conjectures
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operation
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postulate
Explanation
It is possible to produce a finite straight continuously in a straight line.
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.
State whether the following statements are true or false:
Only one line can pass through a given point.
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True
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False
Explanation
Infinite lines can pass through a given point.
So, the statement is false.
State whether the following statements are true or false
A finite line can be extended on its both sides endlessly to get a straight line
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True
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False
Explanation
True,
As per Euclid conceived idea in second axiom which says a finite line can be extended on its both sides endlessly to get a straight line
Greek's emphasised on:
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Inductive reasoning
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Deductive reasoning
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Both A and B
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Practical use of geometry
Explanation
The Greeks were interested in establishing the truth of the statements they discovered using deductive reasoning. A Greek mathematician. Thales is credited with giving the first known proof.
Hence, (b) is the correct answer.
Consider the following statement:
There exists a pair of straight lines that are everywhere equidistant from one another.
Is this statement a direct consequence of Euclid's fifth postulate? Explain
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True
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False
Explanation
Take any line $$l$$ and a point $$P$$ not on $$l$$. Then by play Fair's axiom, which is equivalent to the fifth postulate, we know that there is a unique line m through $$P$$ which is parallel to $$l$$.
Now, the distance of a point from a line is the length of the perpendicular from the point to the line. This distance will be the same for any point on $$m$$ from $$l$$ and any point on $$l$$ from $$m$$. Thus these two lines are everywhere equidistance from one another.
State whether the following statements are true or false
From the fig, $$AB > AC$$
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True
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False
Explanation
The statement is true as
$$AB=AC+BC$$
$$\Rightarrow$$ $$AC$$ is a part of $$AB$$
According to Euclid's fifth axiom the whole thing is greater then a part
$$\therefore AB>AC$$
Things which are equal to the same thing are _____ to one another.
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Perpendicular
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Not equal
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Equal
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Parallel
Explanation
Let $$A$$ and $$B$$ both be equal to $$C$$
$$\Rightarrow A=C ; B=C$$
From this we can clearly say that, $$A=B=C$$
Hence, things which are equal to the same thing must be equal to one another.
Two distinct points in a plane determine ______ lines.
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Unique
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Two
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Three
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None of these
Explanation
According to Euclid's Axioms, For every two points, $$A,\,B$$ there exists no more than one line that contains each of the points $$A,B$$.
Therefore, a unique line can be made from two distinct points.
According to Euclid, a surface has ____.
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Length but no breadth and thickness
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Length and breadth but no thickness
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No length, no breadth and no thickness
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Length, breadth and thickness
Explanation
According to Euclid a surface is a two-dimension plane without any volume, hence it has length and breath but no thickness.
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