Tag: euclid's fifth postulate

Questions Related to euclid's fifth postulate

Identify the given statement: It is possible to produce a finite straight continuously in a straight line.

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

  1. theroem

  2. conjectures

  3. operation

  4. postulate

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Correct Option: D
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.

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

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

  1. consistent

  2. inconsistent

  3. Only (i) & (ii) are consistent

  4. Only  (iii) is consistent

Show answer
Correct Option: A
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.

State whether the following axioms are True or False:

If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^{\circ}$180o.

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: A
Explanation:

If a ray stands on a line, then the sum of two adjacent angles so formed is 180.Conversely if the sum of two adjacent angles is 180, then a ray stands on a line (i.e., the non-common arms form a line).

Hence the above statement is True

If $a=60$ and $b=a$, then $b=60$ by

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

  1. Axiom $1$

  2. Axiom $2$

  3. Axiom $3$

  4. Axiom $4$

Show answer
Correct Option: A
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 $Axiom1$

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

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: A
Explanation:

True,

As per Euclid conceived idea in second axiom a finite line can be extended on its both sides endlessly to get a straight line

State whether the following statements are true or false:
Only one line can pass through a given point.

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:

Infinite lines can pass through a given point.

So, the statement is false.

Two distinct points in a plane determine ______ lines.

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

  1. Unique

  2. Two

  3. Three

  4. None of these

Show answer
Correct Option: A
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.

Things which are equal to the same thing are _____ 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. Perpendicular

  2. Not equal

  3. Equal

  4. Parallel

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Correct Option: C
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.

Things which are halves of the _____ things 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. Same

  2. Different

  3. Two

  4. None of these

Show answer
Correct Option: A
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 things which are halves of the same things then, they are equal to one another.

By applying Euclid's division lemma $72$ and $28$ can be expressed as

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

  1. $28 = (72 - 16) \times 2$

  2. $72 = (28 \times 2) + 16$

  3. $72 = (28 \times 2) - 16$

  4. $16 = 72 - (28 + 2)$

Show answer
Correct Option: B
Explanation:

Solution:

According to Euclid's division lemma if $a$ and $b$ are two numbers then they can be expressed as $b=ap+r.$
Therfore,
$72$ and $28$ can be expressed as
$72=(28\times2)+16$
So, $B$ is the correct option.