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Constructions Maths - Constructions

Jharkhand Board (JAC) - STD 10 - Maths (Jharkhand - English Medium). 21 questions in this chapter.

Question types

Constructions question types

21 questions across 3 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

21
Questions
3
Question groups
5
Question types
Sample Questions

Constructions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.
To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that $\angle\text{BAX}$ is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is:
  • A
    8
  • B
    10
  • C
    11
  • ✓
    12

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.
To construct a triangle similar to a given $\triangle\text{ABC}$ with its sides $\frac{8}{5}$ of the corresponding sides of $\triangle\text{ABC}$ draw a ray BX such that $\angle\text{CBX}$ is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is:
  • A
    5
  • ✓
    8
  • C
    13
  • D
    3

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $\triangle ABC$. first draw a ray BX such that $\angle CBX$ is an acute angle and $X$ lies on the opposite side of $A$ with respect to $B C$. Then locate points $B_1, B_2, B_3, \ldots$ on $B X$ at equal distances and next step is to join:
  • A
    $B _{10}$ to $C$
  • B
    $B _3$ to $C$
  • ✓
    $B _7$ to $C$
  • D
    $B _4$ to $C$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be:
  • A
    135°
  • B
    90°
  • C
    60°
  • ✓
    120°

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark
Choose the correct answer from the given four options.
To divide a line segment $A B$ in the ratio $5: 6$, draw a ray $A X$ such that $\angle B A X$ is an acute angle, then draw a ray $B Y$ parallel to $A X$ and the points $A_1, A_2, A_3, \ldots$ and $B_1, B_2, B_3, \ldots$ are located at equal distances on ray $A X$ and $B Y$, respectively. Then the points joined are:
  • ✓
    $A _5$ and $B _6$
     
  • B
    $A _6$ and $B _5$
     
  • C
    $A _4$ and $B _5$
     
  • D
    $A _5$ and $B _4$

Answer: A.

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Q 6True False[1 Marks ]1 Mark
Write True or False and give reasons for your answer in each of the following.
A pair of tangents can be constructed from a point P to a circle of radius 3.5cm situated at a distance of 3cm from the centre.
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Q 7True False[1 Marks ]1 Mark
Write True or False and give reasons for your answer in each of the following.
A pair of tangents can be constructed to a circle inclined at an angle of 170°.
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Q 8True False[1 Marks ]1 Mark
Write True or False and give reasons for your answer in each of the following.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$, draw a ray $B X$ making acute angle with $B C$ and $X$ lies on the opposite side of $A$ with respect to $B C$. The points $B_1, B_2, \ldots, B_7$ are located at equal distances on $B X, B_3$ is joined to $C$ and then a line segment $B_6 C^{\prime}$ is drawn parallel to $B_3 C$ where $C^{\prime}$ lies on BC produced. Finally, line segment $A ^{\prime} C ^{\prime}$ is drawn parallel to AC .
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Q 9True False[1 Marks ]1 Mark
Write True or False and give reasons for your answer in each of the following.
By geometrical construction, it is possible to divide a line segment in the ratio $\sqrt{3}:\frac{1}{\sqrt{3}}.$
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Q 105 Marks Questions5 Marks
Draw a parallelogram ABCD in which BC = 5cm, AB = 3cm and $\angle\text{ABC}=60^\circ,$ divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD'C' similar to $\triangle\text{BDC}$ with scale factor $\frac{4}{3}.$ Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?
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Q 125 Marks Questions5 Marks
Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to ABC in which PQ = 8cm. Also justify the construction.
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Q 135 Marks Questions5 Marks
Draw a triangle $\triangle\text{ABC}$ in which AB = 5cm, BC = 6cm and ABC= 60º. Construct a triangle similar to $\triangle\text{ABC}$ with scale factor $\frac{5}{7}.$ Justify the construction.
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Q 145 Marks Questions5 Marks
Draw a triangle $\triangle\text{ABC}$ in which AB = 4cm, BC = 6cm and AC = 9cm. Construct a triangle similar to $\triangle\text{ABC}$ with scale factor $\frac{3}{2}.$ Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.
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