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Introduction to Euclid's Geometry Test - 3

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Introduction to Euclid's Geometry Test - 3
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  • Question 1
    1 / -0
    In the given figure, lines AB and CD are intersected by another line PQ. If AB and CD intersect each other on the RHS of PQ, which of the following measures of angles cannot be the value of 1 + 2?

    Solution
    Since 1 and 2 are co-interior angles and lines AB and CD intersect each other on the RHS of PQ, so these are not parallel. Also, the sum of co-interior angles is 180° only when the lines are parallel.
  • Question 2
    1 / -0
    P is a point on a plane. How many lines can pass through P?
    Solution
    Infinitely many lines can pass through a single point as shown in the figure.

  • Question 3
    1 / -0
    Which of the following statements is true?
    Solution
    A point has no dimensions.
  • Question 4
    1 / -0
    If a line AB coincides with another line PQ, which of the following relationships is true?
    Solution
    Coinciding lines overlap each other and two lines can be overlapped if their lengths are equal.
    OR
    By Euclid's axiom, things that coincide with one another are equal to one another.
  • Question 5
    1 / -0
    Two points A and B lie on a plane. How many different lines can pass through A and B both?
    Solution
    As by Euclid's axiom, for two distinct points given, there is a unique line that passes through them.



    From figure also, it is clear that only one line passes through points A and B in a plane.
  • Question 6
    1 / -0
    A solid has ________.
    Solution
    A solid has a definite shape and volume.
  • Question 7
    1 / -0
    If a = b and c = d, which of the following relationships is true?
    Solution
    If a = b and c = d, then a – c = b – d [By Euclid's axiom, if equals are subtracted from equals, the remainders are equal.]
  • Question 8
    1 / -0
    Which of the following statements is true?
    Solution
    By Euclid's postulate 3, a circle can be drawn with any centre and any radius.
  • Question 9
    1 / -0
    A plane has ________.
    Solution
    A plane has two dimensions, i.e. length and breadth.
  • Question 10
    1 / -0
    If a = m and b = n, then which of the following relationships is true?
    Solution
    If a = m and b = n
    a + b = m + n [If equals are added to equals, then wholes are equal.]
  • Question 11
    1 / -0
    Draw a line AB and mark a point P at some distance from it. How many lines can be drawn through 'P' that are parallel to AB?
    Solution
    By Euclid's Playfair's axiom, for every line '' and for every point 'P', not lying on '', there exists a unique line 'm' passing through 'P' and parallel to ''.
  • Question 12
    1 / -0
    When two lines intersect, we get
    Solution
    When two lines intersect, we get a point.
    For example, in the figure, when line intersects line m, we get a point P.

  • Question 13
    1 / -0
    In the given figure, AB = BD. If BP = PD, then which of the following relationships is true?

    Solution
    AP = AB + BP

    = BD + PB [ AB = BD]
    = BP + PD + PB
    = PD + PD + PD [ BP = PD]
    AP = 3PD
  • Question 14
    1 / -0
    Which of the following statements is true?
    Solution
    By Euclid's postulate 2, a terminated line can be produced indefinitely on both the sides.
  • Question 15
    1 / -0
    If a = d, b = c, e = f and m = n, which of the following relationships is true?
    Solution
    If a = d, b = c, e = f and m = n, then a + b = c + d. [By Euclid's axiom, if equals are added to equals, then wholes are equal.]
  • Question 16
    1 / -0
    Which of the following statements is false?
    Solution
    The part is not greater than the whole.
    Rather the whole is greater than the part. [By Euclid's axiom]
  • Question 17
    1 / -0
    Euclid's fifth postulate gives an idea about
    Solution
    Euclid's fifth postulate gives an idea about parallel and intersecting lines. According to the fifth postulate, 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 two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
  • Question 18
    1 / -0
    There are two concentric circles. The radius of the outer circle is 12 cm. Which of the following measurements cannot be the radius of the inner circle?
    Solution
    As the radius of the outer circle (12 cm) is always greater than the inner circle, the inner concentric circle cannot have radius greater than 12 cm.
    So, 13 cm cannot be the radius of the inner circle.
  • Question 19
    1 / -0
    If a = 2b and b = 4c, then which of the following relationships is true?
    Solution
    If a = 2b and b = 4c
    a = 2b
    a = 2(4c) [ b = 4c]
    a = 8c
  • Question 20
    1 / -0
    How many points are common between two distinct lines?
    Solution
    Two distinct lines can have no common point. If they are not intersecting, then they are parallel.
    Two distinct lines can have one distinct point, if they are intersecting lines, i.e. two lines intersect at only one point.
    Hence, the answer is '0 or 1'.
  • Question 21
    1 / -0
    Which of the following statements is true?
    Solution
    According to Euclid, "A straight line lies evenly with all points on itself".
  • Question 22
    1 / -0
    In the given figure, AB = CD. Which of the following relationship is true?

    Solution
    AB = CD (given)



    Adding BC to each side,
    AB + BC = BC + CD
    AC = BC + CD [ AB + BC = AC]
  • Question 23
    1 / -0
    In the given figure, AB = CD = EF.



    Choose the correct relationship among the following.
    Solution
    Given:
    AB = CD … (1)
    CD = EF … (2)



    Now, adding these two equations,
    AB + CD = CD + EF
    = EF + EF [ CD = EF]
    = 2EF
  • Question 24
    1 / -0
    If a + b = 2c, b + c = 2d and c = d, then which of the following relationships is true?
    Solution
    Given:
    a + b = 2c … (1)
    b + c = 2d ... (2)
    c = d … (3)
    From (1) and (2),
    a - c = 2c - 2d
    a - d = 2d - 2d [ c = d from (3)]
    a - d = 0
    a = d
  • Question 25
    1 / -0
    Which of the following statements is true?
    Solution
    A surface is that which has length and breadth only.
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