Tag: euclid's fifth postulate

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

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

  1. first axiom

  2. second axiom

  3. third axiom

  4. fourth axiom
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
Multiple choice maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

The total number of propositions in the Elements are

  1. $465$
  2. $460$
  3. $13$
  4. $55$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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.

  1. Equal sales in September

  2. Unequal sales in September

  3. Ambiguous

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. True

  2. False

  3. Ambiguous

  4. Data Insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

State true or false:

The statements that are proved, are called axioms.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. Axiom 5

  2. Axiom 3

  3. Axiom 2

  4. Axiom 1
Reveal answer Fill a bubble to check yourself
B Correct answer
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".