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Constructions Test - 1

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Constructions Test - 1
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  • Question 1
    1 / -0
    AB is a line segment of a given measure. Which of the following points lies on the perpendicular bisector of AB?

    Solution
    The perpendicular bisector of a line segment is a line segment that falls perpendicularly on the mid point of the line segment. Therefore, point R lies on the perpendicular bisector of AB.
  • Question 2
    1 / -0
    In the given figure, PQ is a line segment of a given measure. The perpendicular bisector of PQ will pass through the point(s) ____.

    Solution
    Perpendicular bisector of PQ will pass through point B as perpendicular bisector passes through the mid point of the line segment, and B is the mid point of line segment PQ.
  • Question 3
    1 / -0
    Which of the following figures show (s) the perpendicular bisector of a line segment AB?

    Solution
    Perpendicular bisector is the line, which falls perpendicularly on the mid point of the line segment.
  • Question 4
    1 / -0
    In the given figure, MN is a perpendicular bisector of PQ.



    Which line segment will be intersected by the perpendicular bisector of OQ?
    Solution
    The perpendicular bisector of OQ will intersect OQ because perpendicular bisector of OQ will pass through the mid point of OQ.
  • Question 5
    1 / -0
    Mukesh constructed a line segment of 32 cm and divided it into four equal parts. The measure of the length of each part is _____.
    Solution
    The line segment of 32 cm is divided into four equal parts. Then, the length of each part = = 8 cm
  • Question 6
    1 / -0
    During construction, while drawing a perpendicular bisector of a line segment, which of the following instruments is/are not used?
    Solution
    Protractor is not used while drawing a perpendicular bisector of a line segment.
  • Question 7
    1 / -0
    PR is a line segment of a given measure. The perpendicular bisector of PR divides the line segment into _____.
    Solution
    The perpendicular bisector is a line segment, which divides the line segment into two equal portions.
  • Question 8
    1 / -0
    In the given figure, the perpendicular bisectors of the given line segments AO and AB are drawn.



    Which of the following points are equidistant from point O?
    Solution
    The points P and Q are equidistant from O, because they are the points of intersection of arcs drawn from A and B on both sides of AB.
  • Question 9
    1 / -0
    Which of the following options is a property of the perpendicular bisector of a line segment?
    Solution
    The perpendicular bisector is a line segment, which falls perpendicularly at the mid point of the line segment.
  • Question 10
    1 / -0
    How many perpendicular bisectors of a line segment can be drawn?
    Solution
    Only one perpendicular bisector of a line segment can be drawn.
  • Question 11
    1 / -0
    In the given figure, which rays represents the angle bisector of ABC?

    Solution
    BX is the angle bisector of angle ABC.
  • Question 12
    1 / -0
    PQR is an angle of a given measure.



    In order to make an angle bisector of PQR, from which two points will you cut the arcs?
    Solution
    The intersecting point of the arcs, drawn from M and N, will be joined with Q in order to get an angle bisector of PQR.
  • Question 13
    1 / -0
    In the figure, BX is an angle bisector of ABC. The angle bisector of ABX will pass through.

    Solution
    The angle bisector of ABX will pass through the arc MN, as it is the arc of ABX.
  • Question 14
    1 / -0
    Which point (s) lie (s) on an angle bisector of a given angle?

    Solution
    OB is the angle bisector of AOC, and point G lies on it.
  • Question 15
    1 / -0
    Ashok constructed an angle of measure x0. He had also drawn an angle bisector of this angle. What will be the measure of each part of the angle bisector?
    Solution
    The angle bisector is a ray, which divides the angle into two equal angles. So, the measure of angle of each part of bisector will be ()0.
  • Question 16
    1 / -0
    Which of the following diagrams show an angle bisector of a given angle?

    Solution
    The angle bisector is a ray, which bisects the angle. So, figure (a), (b) and (c) show the angle bisector of the given angle.
  • Question 17
    1 / -0
    In the figure, bisector of an angle is drawn.



    The measure of angle YOB is
    Solution
    OY is the angle bisector of XOB.
    YOB = XOB
  • Question 18
    1 / -0
    In the following figure, identify the angle bisector rays.


    Solution
    Ray OD is the angle bisector of AOC.
  • Question 19
    1 / -0
    Which of the following is a property of an angle bisector of an angle?
    Solution
    The angle bisector of an angle divides the angle into two equal halves.
    It bisects the angle in ratio 1 : 1.
  • Question 20
    1 / -0
    How many angle bisectors of a given angle can be drawn?
    Solution
    There can be only one angle bisector of a given angle.
  • Question 21
    1 / -0
    Which of the following diagrams show an angle of measure 1200?

    Solution
    (a), (b) represent angles of 120°.
  • Question 22
    1 / -0
    Mohan constructs a triangle with a base angle of 300. He constructed this angle by
    Solution
    By bisecting angle between 0° and 60°, we get a 30° angle as = 30°
  • Question 23
    1 / -0
    Which of the following diagrams does not represent an angle of 600?

    Solution
    Figure (d) represents angle of 120° and not 60°.
  • Question 24
    1 / -0
    Which of the following steps will give you an angle of 1200?
    Solution
    By bisecting 60° and 180°, we get 120°.
    i.e. = 120°
  • Question 25
    1 / -0
    Which of the following angles cannot be constructed by a ruler and a compass?
    Solution
    The angle, which is divisible by 15, can be drawn with the help of ruler and compass only.
    Since 25° is not divisible by 15, C is the correct option.
  • Question 26
    1 / -0
    Which of the following angles can be made without bisecting the two angles?
    Solution
    Angle of measure 120° can be drawn without bisecting the two angles.

  • Question 27
    1 / -0
    Which of the following figures represent(s) an angle of 450?

    Solution
    Figure c shows the angle of 450.
  • Question 28
    1 / -0
    If you bisect an angle between 600 and 900, which of the following angles will be constructed?
    Solution
    By bisecting 60° and 90°, we get = 75°.
  • Question 29
    1 / -0
    Which of the following diagrams represent (s) an angle of 300?

    Solution
    The figure (b) represents 30° because it is constructed by bisecting the angle between 0° and 60°.
  • Question 30
    1 / -0
    If you bisect an angle between 600 and 1200, the angle formed is
    Solution
    If we bisect angle between 60° and 120°, we get
    = = 90°, which is a right angle.
  • Question 31
    1 / -0
    During the construction of a 750 angle, which of the following procedures a student can adopt?

    (1) 900 - 150 (2) 600 + 150 (3) 300 + 450 (4) 450 - 300
    Solution
    The angle of 75° can be constructed by 90° - 15°, 60° + 15°, 30° + 45°.
  • Question 32
    1 / -0
    In the given figure, AOB =



    In order to make an angle + , which steps will you prefer?
    Solution
    For making angle, we will prefer the construction of an angle on the arm OB.
  • Question 33
    1 / -0
    A student of class IX constructed an angle of 900 = 600 + 300. Which step will he use to make an angle of 750?
    Solution
    By bisecting the 30° part, we will get angle of measure 15°, and 60° + 15° will give us 75°.
  • Question 34
    1 / -0
    In the given figure, BOA = 0.



    If an angle of measure is drawn in the above figure, then which of the following figures is correct?

    Solution
    By adding the two angles ( - and), we will get.
    In figure (a),
    AOB = BOP + POA
    = + –
    =
  • Question 35
    1 / -0
    In the figure, the measure of an angle AOB is

    Solution
    AOB = = = 105°
  • Question 36
    1 / -0
    Ashok constructed an angle, 120° = 90° + 30°. In order to make an angle of 105°, which step will he follow?
    Solution
    Ashok constructed an angle, 120° = 90° + 30°.
    By bisecting angle of 30°, we will get an angle of 15°.
    Then, 90° + 15° gives 105°.
  • Question 37
    1 / -0
    A student constructed an angle, 150° = 120° + 30°. In order to form an angle of 135°,
    Solution
    150° = 120° + 30°
    By bisecting angle of 30°, we will get angle of 15°.
    Then, 120° + 15° gives 135°.
  • Question 38
    1 / -0
    In the given figure, AOB = .



    An angle of measure, – is constructed on it. What will be the measure of POA?
    Solution
    AOB = BOP + POA
    = + POA (As given)
    – = POA
    POA =
  • Question 39
    1 / -0
    In the given figure, if we bisect an arc ED, the angle formed will be

    Solution
    ED is the arc of 60° and 90° angles.
    Then, by bisecting these angles, we will get .
  • Question 40
    1 / -0
    A student constructed an angle of measure 1050 by constructing an angle bisector.. In order to make 1050, he has to construct the angles and . The measures of and are
    Solution
    By bisecting the angle between 90° and 120°, we will get an angle of 105° [= 105°].
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