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

Which of the following is Euclid's first postulate?

  1. All right angles are equal to one another.

  2. The whole is greater then the part.

  3. A circle can be drawn with any centre and any radius.

  4. A straight line segment can be drawn joining any two points.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Euclid's first postulate is :

A straight line segment can be drawn joining any two points.
Thus, option D is correct.

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

If point $P$ lies on $AB$, then $AB$ is always greater than $AP$. This concept is on which of the following Euclid's Axioms.

  1. First Axiom

  2. Second Axiom

  3. Third Axoim

  4. Fifth Axiom
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The fifth axiom of Euclid's about geometry is the whole of anything is greater than the part of it.

Here AB is the whole line and AP is the part and according to the fifth axiom we have AB is always greater than AP.
So the given statement is Euclid's fifth axiom.

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 statement is true/false

Use Euclid's division lemma we can show that the square of any positive integer is either of the form $3m$ or $3m+1$ for some integer m.

  1. True

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

According to Euclid's division lemma, any integer n can be written as 3q, 3q+1, or 3q+2. Squaring these yields 9q^2 (3m), 9q^2+6q+1 (3m+1), and 9q^2+12q+4 (3m+1), confirming the statement.

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

Axioms are assumed

  1. universal truths in all branches of mathematics

  2. universal truths specific to geometry

  3. theorems

  4. definitions
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From time immemorial, axioms have been acquired by man through the day to day experiences .

No mathematical deduction is needed to prove them.
Practically they are starting points of reasoning.

So axioms are assumed universal truths in all branches of mathematics.

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

John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid's axiom that illustrates the relative ages of John and Ram

  1. First axiom

  2. Second axiom

  3. Third axiom

  4. Fourth axiom
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given that
John's age=Mohan's age &
Ram's age=Mohan's age.
So, by the first axiom of Euclid, 
John's age=Ram's age.
Euclid's first axiom states that
things, which are equal to the same thing, are equal to one another.

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

$\angle A=\angle B$ and $\angle B=\angle C$, According to which axiom of Euclid the relation between $\angle A$ and $\angle C$ is established?

  1. I

  2. II

  3. III

  4. IV
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that $\quad \angle A=\angle B\quad & \quad \angle B=\angle C.\quad $

Then, according to Euclid's first axiom, which states that 
"things which are   equal to the same thing are also equal to each other",
 $\quad \angle A=\angle C\quad $
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

Euclid's fourth axiom says that everything equals itself.

  1. True

  2. False

  3. Ambiguous

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

Euclid's fourth axiom states that "things which coincide with one another are equal to one another."

So the given statement is true by the axiom IV.
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

The Euclidean geometry is valid only for figures in the plane.

  1. True

  2. False

  3. Ambiguous

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

The given statement is true. Because,  by Einstein's  theory of  general  relativity, physical space itself is not Euclidean. Euclidean space is a good approximation  for it where the gravitational field is weak.  

So, in space or in multidimensional space the Euclidean axioms are not applicable.
Ans- Option A.