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Introduction to Euclids Geometry Test - 11

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Introduction to Euclids Geometry Test - 11
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  • Question 1
    1 / -0
    Which Euclid's postulate led to the discovery of several other geometries while attempting to prove it using other postulates and axioms
    Solution
    Attempts to prove Euclid's Fifth Postulate using other postulates and axioms led to the discovery of several others geometries
  • Question 2
    1 / -0
    Euclid stated that if equals are subtracted from equals, the remainders are equals in the form of :
    Solution
    The above statement is Euclid's third axiom which states that If equals are subtracted from equals, the remainders are equal.
    So, $$A$$ is correct.
  • Question 3
    1 / -0
    Two intersecting lines cannot be parallel to the same line is stated in the form of :
    Solution
    Axiom
    example if line A and line B are intersecting and line C is parallel to line A then line C is not parallel to line B.
    $$A$$
  • Question 4
    1 / -0
    Euclid's fifth postulate is
    Solution
    The fifth postulates of Euclid is
    if a straight line, falling on two straight lines, makes the interior angles on the same side of it together less than two right angles, then the two strait lines, if produces indefinitely, meet on that side on which the sum of the angles is less than two right angles. 
    Ans- Option D.
  • Question 5
    1 / -0
    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.
    Solution
    Given that,
    John's age $$=$$ Mohan's age &
    Ram's age $$=$$ Mohan's age.
    Euclid's first axiom states that, things which are equal to the same thing, are equal to one another.
    So, by the first axiom of Euclid, 
    John's age $$=$$ Ram's age.

    Hence, Euclid's first axiom is applicable here.
  • Question 6
    1 / -0
    Euclid's stated that all right angles are equal to each other in the form of :
    Solution
    One of Euclid's five postulates is:
    $$All$$ $$right$$ $$angles$$ $$are$$ $$CONGRUENT$$.
    So, the correct option is  $$C$$.
  • Question 7
    1 / -0
    The things which are double of same thing are :
    Solution
    According to an Euclidian axiom, 
    The things which are double of the same things are equal to one another.
    Example : if $$2x=2y,$$ then $$x=y$$.
    Hence, option A is correct.
  • Question 8
    1 / -0
    Euclidean geometry is valid only for curved surfaces.
    Solution
    Euclid's postulates:

    $$\Rightarrow$$ A straight line can be drawn joining any two points.

    $$\Rightarrow$$ A straight line segment can be extended indefinitely in a straight line.

    $$\Rightarrow$$ A circle can be drawn having the segment as radius and one endpoint as center. 

    $$\Rightarrow$$ All right angles are congruent and equal.

    $$\Rightarrow$$ Parallel postulate.

    Hence, we can observe that euclidian geometry is valid for 2-dimensional geometrical figures.
  • Question 9
    1 / -0
    Axioms are assumed
    Solution
    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.
  • Question 10
    1 / -0
    The things which coincide with one another are:
    Solution
    According to Euclid's postulates, $$\text{equal}$$ things coincide with each other.
    Hence, $$A$$ is correct.
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