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Constructions Test - 5

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Constructions Test - 5
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Weekly Quiz Competition
  • Question 1
    1 / -0

    The orthocentere of an obtuse triangle lies ___________.

    Solution

    This is so because orthocentre of a triangle is the point of intersection of the three altitudes of a triangle and as we know, the three altitudes of an obtuse triangle meet outside the triangle .

    Thus, the orthocentre of an obtuse triangle is outside the triangle.

  • Question 2
    1 / -0

    With the help of a ruler and compass. It is possible to construct an angle of _____.

    Solution

    With the help of a ruler a compass, we can only construct an angle which is a multiple of 150 and  as 22.50 is a multiple of 150, So, we can construct it. 

  • Question 3
    1 / -0

    The construction of a triangle ABC in which AB = 2.5 cm, ∠A = 450 is not possible when difference of BC and AC is equal to ______.

    Solution

    To construct a triangle whose base, base angle and difference of other two sides are given , the difference of other two sides must be less than the base of the triangle.

    But in this case BC - AC > AB, So, we can not construct it.

  • Question 4
    1 / -0

    The construction of △ABC, given that BC = 5 cm, ∠B = 450 is not possible when difference of AB and AC is equal to __________.

    Solution

    To construct a triangle whose base, base angle and difference of other two sides are given, the difference of other two sides should be less than its base.

    But , here, AB - AC > BC, So we can not construct it.

  • Question 5
    1 / -0

    The construction of a △ABC, given that BC = 4 cm, ∠C = 600 is possible when difference of AB and AC is equal to

    Solution

    To construct a triangle, whose base, base angle and difference of other two sides are given, the difference of other two sides must be less than its base.

    As in this case, AB - AC < BC, so, it is possible to construct it.

  • Question 6
    1 / -0

    To construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm. We draw line segment AB of 12 cm. Draw a ray AX making 900 with AB. The next step is:

    Solution

    We will cut the line segment of length equal to the hypotenus of the triangle i.e. 18 cm . Now the line segment AD thus formed will be the hypotenus of the triangle.

  • Question 7
    1 / -0

    By following these steps of construction,
    (i) Draw a line segment PQ = 11 cm
    (ii) At P construct an angle of 600 and at Q, an angle of 450,
    (iii) Bisect these angles. Let the bisectors of these angles intersect at a point A.
    (iv) Draw perpendicular bisectors DE of AP to intersect PQ at B and FG of AQ to intersect PQ at C.
    (v). Join AB and AC. △ABC has been obtained. In this △ABC, 

    Solution

    We can say that AB + BC + CA = 11cm, because the steps given above are the steps to construct a triangle when perimeter of a triangle and its two angles are given.

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