Tag: introduction to euclid's geometry

Questions Related to introduction to euclid's geometry

The mathematical statements that are proved are called axioms.

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

  3. cannot be determined

  4. None of the above

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Correct Option: B
Explanation:

False, statements that are proved are theorems.

A proof is required for :

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

  1. Postulate

  2. Axiom

  3. Theorem

  4. Definition

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Correct Option: C
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.

A lemma is a proven statement used for proving another statement.

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:

'Lemma ' is a subsidiary or intermediate theorem in an argument or proof.

A theorem is:

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

  1. an assumption

  2. always true

  3. always false

  4. sometimes true and sometimes false

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Correct Option: B
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 $180^o$

Complete the sentence with the most suitable option:
She wishes she _________ younger than she is.

english basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. Were

  2. Would be

  3. Had been

  4. Is

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Correct Option: A

Complete the sentence with the most suitable option:
I wish we _____________ late for this film. I can't follow the story.

english basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. Didn't arrive

  2. Hadn't arrived

  3. Wouldn't arrive

  4. Wouldn't have arrived

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Correct Option: B

Complete the sentence with the most suitable option:
I wish our school __________ a bigger library than it has.

english basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. Had had

  2. Would have

  3. Had

  4. Will have

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Correct Option: C

Complete the sentence with the most suitable option:
If only you _________ less noise.

english basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. Had made

  2. Made

  3. Would make

  4. Might make

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Correct Option: B

Complete the sentence with the most suitable option:
He wished his father ______________ him some shoes before the new term starts.

english basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. Was buying

  2. Was going to buy

  3. Would buy

  4. Had bought

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Correct Option: C

Complete the sentence with the most suitable option:
A: Janet couldn't come to the concert last night.
B: I wish she _______________.

english basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. Is able to come

  2. Was able to come

  3. Could have come

  4. Had come

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Correct Option: C