Tag: euclid's postulates

Questions Related to euclid's postulates

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

  1. Postulate III $\quad$ A terminated line can be produced indefinitely

  2. Postulate II $\quad$ All right angles are equal to one another

  3. Postulate IV $\quad$ A circle can be drawn with any centre and any radius

  4. Postulate I $\quad$ A straight line may be drawn from any one point to any other point.

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Correct Option: D
Explanation:

Postulates 
1. A straight line may be drawn from any point to any other point. 
2. A terminated line (line segment) can be produced indefinitely.
 3. A circle may be described with any centre and any radius. 
4. All right angles are equal to one another. 
5. If a straight line falling on two straight lines makes the interior angles on the same side of it, taken together less than two right angles
So, (D) option is correct.
Answer (D) Postulate I  A straight line may be drawn from any one point to any other point.

Identify the given statement: A circle can be described with any given center and radius.

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

  1. postulate

  2. conjectures

  3. theorem

  4. operation

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Correct Option: A
Explanation:
A circle can be described with any given center and radius.
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.

_______ is another name for postulate.

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. axiom

  4. operation

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Correct Option: C
Explanation:

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.


A statement accepted as true as the basis for argument or inference, is

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

  1. Axioms

  2. Conjecture

  3. Corollary

  4. Theorem

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Correct Option: A
Explanation:
A statement accepted as true as the basis for argument or inference, is axioms.

Let us consider an axiom of addition and multiplication.
Let $x$ and $y$ be real numbers.
Then $x + y$ is also a real number and $xy$ is also a real number.

It is possible to draw a straight line from any point to any other point. Identify the given statement is _________.

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. postulate

  4. operation

Show answer
Correct Option: C
Explanation:
It is possible to draw a straight line from any point to any other point. 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.

Which of the following is NOT a Euclid's postulate?

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

  1. We can describe a circle with any center and radius

  2. All right angles are equal to one another

  3. There is a unique line that passes through two given points

  4. Through a point not on a given line, exactly one parallel line may be drawn to the given line

Show answer
Correct Option: D
Explanation:

Following statement is not a Euclid's postulate:-

Through a point not on a given line, exactly one parallel line may be drawn to the given line.

Two lines can intersect in _____ points.

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

  1. $0$

  2. $1$`

  3. $2$

  4. infinite

Show answer
Correct Option: A,B,D
Explanation:

Two lines can intersect at one point

EX:
$3x+4y=2$

$3x+9y=8$
Two lines can intersect at no point (parallel lines)
$3x+4y=2$
$3x+4y=5$
Two lines can intersect at infintie points 
Both lines lie on each other (same lines)
$3x+4y=2$
$6x+8y=4$

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. Either

  4. Neither

Show answer
Correct Option: A
Explanation:

This set of axiom is consistent.
(i) If a=b and b=c then a =c
(ii) If a = b and c = d then a+ b =c +d
(iii) If x = 2y and z = 2y then x = z

Which of the following needs a proof?

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

  1. Theorem

  2. Axiom

  3. Definition

  4. Postulate

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Correct Option: A
Explanation:

Axiom, Postulate and definition are self evident & do not need any proof.

Theorem is a proposition which needs a proof to establish its truth.
Ans- Option A.

Two distinct lines cannot have more than one point in common.

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

  1. True

  2. False

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Correct Option: A
Explanation:

Here we are given two lines l and m. We need to prove that they have only one point in common.For the time being, let us suppose that the two lines intersect in two distinct points, say P and Q. So, you have two lines passing through two distinct points P and Q. But this assumption clashes with the axiom that only one line can pass through two distinct points. So, the assumption that we started with, that two lines can pass through two distinct points is wrong. From this, what can we conclude? We are forced to conclude that two distinct lines cannot have more than one point in common.