Tag: conditional statements and converse

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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

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

  1. theroem

  2. conjectures

  3. operation

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

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

  1. consistent

  2. inconsistent

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

  4. Only (iii) is consistent
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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.

  1. True

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

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

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

  1. True

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

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

Two distinct points in a plane determine ______ lines.

  1. Unique

  2. Two

  3. Three

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

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

Things which are equal to the same thing are _____ to one another.

  1. Perpendicular

  2. Not equal

  3. Equal

  4. Parallel
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

Things which are halves of the _____ things are equal to one another.

  1. Same

  2. Different

  3. Two

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

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

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

  1. $28 = (72 - 16) \times 2$
  2. $72 = (28 \times 2) + 16$
  3. $72 = (28 \times 2) - 16$
  4. $16 = 72 - (28 + 2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.