Tag: axioms, postulates and theorems

Quizzes (5) Questions (60)

Questions Related to axioms, postulates and theorems

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

A proof is required for :

  1. Postulate

  2. Axiom

  3. Theorem

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

Axiom/Postulate — a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved. 


Theorem — a mathematical statement that is proved using rigorous mathematical reasoning.  In a mathematical paper, the term theorem is often reserved for the most important results.
  
So, the correct option is $C$ as a theorem needs a proof.

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

A theorem is:

  1. an assumption

  2. always true

  3. always false

  4. sometimes true and sometimes false
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A theorem is a Statement (logic) that has been proved on the basis of previously established statements, such as other theorems, and generally accepted statements.
A theorem is based on assumption that theorem is true.


Example: In a Euclidean space, the sum of measures of the three angles of any triangles is invariably equal to the straight angle, also as $180^o$

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

Select the correct statement for the following:

$A$: The angles of an equilateral triangle are equal.
$B$: Angles opposite to two congruent sides of a triangle are congruent.

  1. $A$ is a theorem and $B$ is its corollary
  2. $B$ is a theorem and $A$ is its corollary
  3. $A$ and $B$ are both theorems
  4. $A$ and $B$ are both corollaries
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$B$ is called the  Triangle theorem.  $A$ can be proved using this theorem, as in an equilateral triangle, all sides are equal and the angles opposite to these congruent sides are Equal. So, $A$ is the corollary of $B$

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

A proof is required for a :

  1. Postulate

  2. Axiom

  3. Theorem

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

Axiom/Postulate — a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved. 


Theorem — a mathematical statement that is proved using rigorous mathematical reasoning.  In a mathematical paper, the term theorem is often reserved for the most important results.

So, the correct option is $C$ as a theorem needs a proof.

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

The formation or expression of an opinion or theory without sufficient evidence for proof is known as

  1. axioms

  2. conjecture

  3. corollary

  4. theorem
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The formation or expression of an opinion or theory without sufficient evidence for proof is known as conjecture.

For example, make a conjecture about the next number in the pattern $2, 6, 11, 17, ...$. The terms increase by $4$, then $5$, and then $6$.
Multiple choice maths axioms, postulates and theorems euclid's fifth postulate conditional statements and converse euclid's postulates

__________ implies to conclude or suppose from grounds or evidence insufficient to ensure reliability.

  1. axioms

  2. conjecture

  3. corollary

  4. theorem
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Conjecture implies to conclude or suppose from grounds or evidence insufficient to ensure reliability.

For example, make a conjecture about the next number in the pattern 2 ; 6 ; 11 ; 17 ; ... The terms increase by 4, then 5, and then 6.
Multiple choice maths axioms, postulates and theorems euclid's fifth postulate conditional statements and converse euclid's postulates

What is a conjecture?

  1. A true statement

  2. A statement that you believe is true based upon your observations

  3. A proven statement about something you believe

  4. A statement used by scientists
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The formation or expression of an opinion or theory without sufficient evidence for proof is known as conjecture. 


Or a conjecture can be stated as a statement that you believe is true based upon your observations.