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Introduction to Euclids Geometry Test - 7

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Introduction to Euclids Geometry Test - 7
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  • Question 1
    1 / -0

    “Lines are parallel if they do not intersect” is stated in the form of

    Solution

     Euclid gave the definition of parallel lines in Book I, Definition 23 just before the five postulates.

  • Question 2
    1 / -0

    The edges of a surface are

    Solution

    Edge is a line or border at which a surface terminates.

  • Question 3
    1 / -0

    The boundaries of the solids are

    Solution

    A solid has shape, size, position and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from the other.

  • Question 4
    1 / -0

    If the point P lies in between M and N, C is the mid-point of MP then

    Solution

    Since, P lies between M and N, MN = MP+PN .....(i)

    Now,C is the mid-point of MP,so, MP=MC+CP

    =>MN = MC+CP+PN

    => MN = MC +CN     (CP+PN =CN)

  • Question 5
    1 / -0

    Axioms are assumed

    Solution

    Axioms are assumed universal truths in all branches of mathematics because axioms are present in all branches of Mathematics.

  • Question 6
    1 / -0

    “Two intersecting lines cannot be parallel to the same line” is stated in the form of

    Solution

    Euclid's fifth postulate can also be stated in the following form: Two distinct intersecting lines cannot be parallel to the same line.

  • Question 7
    1 / -0

    The things which coincide with one another are

    Solution

    "The things which coincide with one another are equal" is one of the axioms given by Euclid. Example:Segment AB = Segment BA ; ∠A = ∠A .

  • Question 8
    1 / -0

    Euclid stated that if equals are added to equals, the wholes are equal in the form of

    Solution

    This is Euclid's second axiom stating addition of equals. An algebraic version of Euclid’s second axiom would read “if x=y, and if a=b, then x + a = y + b.”

  • Question 9
    1 / -0

    Euclid stated that if equals are subtracted from equals, the remainders are equal in the form of

    Solution

    This is Euclid's third axiom stating subtraction of equals. An algebraic version of Euclid’s second axiom would read “if x=y, and if a=b, then x – a = y – b.”

  • Question 10
    1 / -0

    The number of line segments determined by three non-collinear points is

    Solution

    You need two points to draw a line segment. If the points A,B and  are non-collinear,we can draw the lines :AB , AC, BA , BC, CA , CB. Now, line AB is the same as line BA, same for lines AC and CA and BC and CB. So,the lines are: AB, BC and AC ; 3 lines only.

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