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Introduction to Euclids Geometry Test - 13

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Introduction to Euclids Geometry Test - 13
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  • Question 1
    1 / -0
    Two salesmen make equal sales during the month of August. In September, each salesman doubles his/her sale of the month of August. Compare their sales in September.
    Solution
    Let each salesman makes the sale of  Rs. $$x$$ in August.
    As per the question, In September, the sale of each salesman is Rs. $$2x$$.
    According to Euclids sixth axiom, things that are double the same thing are equal to one another.
    So, the sales of each salesman are equal in the month of september
  • Question 2
    1 / -0
    If equals are added to equals, then the wholes are .......
    Solution
    According to the first axiom of Euclid " if equals are added to equals the wholes are equal."
    Ans- Option B.
  • Question 3
    1 / -0
    The things which are double of the same thing are equal to one another.
    Solution
    Let $$a=2x$$ and $$b=2x$$ when $$a, b$$ & $$x$$ are arbitrary numbers or things. 

    The first axiom of Euclid states that :
    "Things which are equal to the same thing are also equal to each other."

    So $$a=b=2x$$
    i.e the given statement is true.
    Ans - Option A.
  • Question 4
    1 / -0
    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
    Solution
    (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.
  • Question 5
    1 / -0
    The edges of a surface are called curves.
    Solution
    The edges of a surface are called curves.
    For example, circle is a plane surface and its edge is the circumference, which is a curve
  • Question 6
    1 / -0
    A ______ is a statement that is accepted without proof.
    Solution
    A postulate is a statement that is accepted without proof.
    Example: A unique straight line can be drawn from any point to any other point.
  • Question 7
    1 / -0
    If $$a=60$$ and $$b=a$$, then $$b=60$$ by
    Solution
    According to Euclid's 1st axiom,- Things which are equal to the same thing are also equal to one another
    So, if $$a=60$$ and $$b=a$$, then $$b=60$$ by $$Axiom1$$
  • Question 8
    1 / -0
    Identify the given statement: It is possible to produce a finite straight continuously in a straight line.
    Solution
    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.
  • Question 9
    1 / -0
    Things which are equal to the same thing are _____ to one another.
    Solution
    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.
  • Question 10
    1 / -0
    ___________ was the most logical and abstract creator of Euclid's geometry approach.
    Solution
    Pythagoras developed the theory of geometry to a great extent.
    Thus Pythagoras was the most logical and abstract creator of Euclid's geometry approach.
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