Tag: euclid's postulates

Questions Related to euclid's postulates

It is known that $x+y=10,$ then $x+y+z=10+z$. The Euclid's axiom that illustrates this statement is

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. first axiom

  2. second axiom

  3. third axiom

  4. fourth axiom

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Correct Option: B
Explanation:
Here z has been added to two quantities  which are equal to each other.
So, by Euclid's second axiom, which states that
if equals are added to equals the wholes are equal,
x+y+z=10+z is true.
Ans- Option B.

The total number of propositions in the Elements are

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. $465$

  2. $460$

  3. $13$

  4. $55$

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Correct Option: A
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.

Euclid belongs to the country

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. Babylonia

  2. Egypt

  3. Greece

  4. India

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Correct Option: C
Explanation:

Euclid belongs to Greece.

Ans- Option C.

The edges of a surface are called curves.

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. True

  2. False

  3. Ambiguous

  4. Data Insufficient

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Correct Option: A
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

Two salesmen make equal during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. Equal sales in September

  2. Unequal sales in September

  3. Ambiguous

  4. None of the above

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Correct Option: A
Explanation:

Let each salesman make Rs. $x$ in August.
In September, the sale of each salesman is Rs. $2x$.
According to Euclids sixth axiom, things which are double of the same thing are equal to one another, the wholes are equal.
So, the sales of each salesman are equal.

The things which are double of the same thing are equal to one another.

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. True

  2. False

  3. Ambiguous

  4. Data Insufficient

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Correct Option: A
Explanation:

Let a=2x   and  b=2x  when a, b & x are arbritary 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.
i.e the given statement is true.
Ans- Option A.

State true or false:

The statements that are proved, are called axioms.

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. True

  2. False

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Correct Option: B
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 theory.
so the given statement is false.
Ans- Option B.

Define the Euclid's axiom which contains following equation
If $x=9$ and $y=1$, then $x-y=8$.

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. Axiom 5

  2. Axiom 3

  3. Axiom 2

  4. Axiom 1

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Correct Option: B
Explanation:
If $x= 9$ and $y= 1$ then $x-y = 8$
The Euclid's axiom used in this statement is Axiom 3 which states that "If equal be subtracted from equal the remainders are equal".

If equals are added to equals, then the wholes are .......

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. unequal

  2. equal

  3. sometimes equal sometimes unequal

  4. nearest to each other

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Correct Option: B
Explanation:

According to the first axiom of Euclid " if equals are added to equals the wholes are equal."

Ans- Option B.

A ______ is a statement that is accepted without proof.

maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

  1. theorem

  2. conjectures

  3. postulate

  4. operation

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Correct Option: C
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.