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Introduction to Euclids Geometry Test - 16

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Introduction to Euclids Geometry Test - 16
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  • Question 1
    1 / -0
    State the Euclid's axiom used in the following statements
    $$AD < AB$$

    Solution

  • Question 2
    1 / -0
    Two distinct ________ lines cannot be parallel to the same line.
    Solution
    Two intersecting lines cannot be parallel to same line as this statement is equivalent to Euclid's fifth postulate.
  • Question 3
    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
    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
  • Question 4
    1 / -0
    Euclid stated that all right angles are equal to one another in the form of a/an ..........
    Solution
    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, then the the two straight lines if

    produced indefinitely, meet on that side on which the sum of angles is taken together

    less than two right angles.

    Euclid used the term postulate for the assumptions that were specific to geometry

    and otherwise called axioms. A theorem is a mathematical statement whose truth

    has been logically established.
    Answer (C) Postulate
  • Question 5
    1 / -0
    _______ is another name for postulate.
    Solution
    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 6
    1 / -0
    A statement accepted as true as the basis for argument or inference, is
    Solution
    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.
  • Question 7
    1 / -0
    Identify the given statement: A circle can be described with any given center and radius.
    Solution
    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.
  • Question 8
    1 / -0
    It is possible to draw a straight line from any point to any other point. The given statement is _________.
    Solution
    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.
  • Question 9
    1 / -0
    Which of the following is NOT a Euclid's postulate?
    Solution
    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.
  • Question 10
    1 / -0
    _____is regarded as the Father of Geometry.
    Solution

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