9th Class Mathematics Constructions Question Bank

done Constructions Total Questions - 10

• question_answer1)
  For which of the following conditions the construction of a triangle is NOT possible?
  A)
   If two sides and one angle is given. done clear
  B)
   If two sides and included angle between them is given. done clear
  C)
   If three sides are given. done clear
  D)
   If two angles and side between them is given. done clear
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• question_answer2)
  The construction of a\[\Delta LMN\]in which LM = 8 cm, \[\angle L={{45}^{o}}\]is possible when (MN + LN) is ___ .
  A)
   6 cm                done clear
  B)
          7 cm                done clear
  C)
   9 cm                done clear
  D)
          5 cm                done clear
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• question_answer3)
  Which of the following angles CANNOT be constructed by using ruler and compass only?
  A)
  \[{{30}^{o}}\] done clear
  B)
         \[{{45}^{o}}\] done clear
  C)
  \[{{70}^{o}}\] done clear
  D)
         \[{{90}^{o}}\] done clear
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• question_answer4)
  The construction of a \[\Delta ABC\] in which BC = 6 cm and \[\angle B={{50}^{o}}\]is NOT possible when (AB - AC) is equal to ___ .
  A)
   5.6 cm                         done clear
  B)
   5 cm                done clear
  C)
   6 cm                done clear
  D)
          4.8 cm             done clear
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• question_answer5)
  Which of the following options is INCORRECT?
  A)
   An angle of \[{{52.5}^{o}}\] can be constructed. done clear
  B)
   A triangle ABC can be constructed in which AB = 5 cm, \[\angle A={{45}^{o}}\]and BC + AC = 5 cm. done clear
  C)
   A triangle ABC can be constructed in which BC = 6 cm, \[\angle C={{30}^{o}}\]and AC - AB = 4 cm. done clear
  D)
   A triangle ABC can be constructed in which \[\angle B={{60}^{o}},\angle C={{45}^{o}}\]and AB + BC + AC = 12 cm. done clear
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• question_answer6)
  Following are the steps of construction of a \[\Delta ABC\]in which AB = 5 cm, \[\angle A={{30}^{o}}\] and AC - BC = 2.5 cm. Arrange them and select the CORRECT option.

  (i) Draw \[\angle BAX={{30}^{o}}\]

  (ii) Draw the perpendicular bisector of BD which cuts AX at C.

  (iii) Draw AB = 5 cm

  (iv) Join BD

  (v)  Join BC to obtain the required triangle ABC

  (vi) From ray AX, cut off line segment AD = AC-BC= 2.5 cm

  A)
  (a\[(i)\to (iii)\to (iv)\to (v)\to (vi)\to (ii)\] done clear
  B)
  \[(iii)\to (i)\to (vi)\to (iv)\to (ii)\to (v)\] done clear
  C)
  \[(iii)\to (i)\to (ii)\to (v)\to (iv)\to (vi)\] done clear
  D)
  \[(iii)\to (ii)\to (iv)\to (i)\to (vi)\to (v)\]  done clear
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• question_answer7)
  State T for true and 'F' for false.

  (i) A triangle whose sides measure 8 cm, 4 cm and 12 cm can be possible.

  (ii) It is possible to construct an angle of \[{{67.5}^{o}}\]using ruler and compass only.

  (iii) It is possible to construct a\[\Delta XYZ\]in which \[\angle X={{60}^{o}},\angle Y={{100}^{o}}\]and\[\angle Z={{20}^{o}}.\]

             
  A)

  (i)	(ii)	(iii)
  T	F	T

                  done clear
  B)

  (i)	(ii)	(iii)
  F	F	F

  done clear
  C)

  (i)	(ii)	(iii)
  F	T	T

                  done clear
  D)

  (i)	(ii)	(iii)
  T	T	F

  done clear
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• question_answer8)
  Let ABC be a triangle in which BC = 5 cm, \[\angle B={{60}^{o}}\]and AC + AB = 7.5 cm. Given below are the steps of constructing the triangle ABC. Which of the following steps is INCORRECT?

  Step I: Draw a line segment BC of length 5 cm.

  Step II: Draw an \[\angle XBC={{60}^{o}}\]at point B of line segment BC.

  Step III: Cut off PB = 3.5 cm on the ray BX.

  Step IV: Join PC.

  Step V: Draw\[\bot \]bisector of BC which intersect ray BX at A. Join AC.

  Step VI: ABC is the required triangle.

  A)
   Step II only done clear
  B)
   Step III only done clear
  C)
   Step II and V done clear
  D)
   Step III and V done clear
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• question_answer9)
  Following are the steps of construction of a rectangle ABCD whose adjacent sides are  of lengths 5 cm and 3.5 cm. Arrange them and select the CORRECT option.

  (p) Draw a line segment BC of length 5 cm.

  (q) With A as centre, draw an arc of radius 5 cm.

  (r) Draw an\[\angle XBC={{90}^{o}}\]at point B of line segment BC.

  (S) Cut a line segment AB = 3.5 cm on \[\overrightarrow{BX}\]

  (T) With C as centre, draw an arc of radius 3.5 cm which intersects the arc at D.

  (U) Join AD and CD.

  A)
  \[(p)\to (s)\to (q)\to (r)\to (u)\to (t)\] done clear
  B)
  \[(p)\to (r)\to (s)\to (q)\to (t)\to (u)\] done clear
  C)
  \[(p)\to (s)\to (r)\to (q)\to (t)\to (u)\] done clear
  D)
  \[(p)\to (q)\to (r)\to (s)\to (u)\to (t)\] done clear
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• question_answer10)
  Step I & Step V are in correct order while constructing an equilateral triangle one of whose altitudes measures 5 cm. Which of the following options is CORRECT while arranging the remaining steps in CORRECT order? Step I : Draw a line XV.

  (i) From\[\angle P,\]set off PA = 5 cm, cutting PQ at A

  (ii) From P, draw \[PQ\bot XY.\]

  (iii) Mark any point P an XY.

  Step V : Construct \[\angle PAB={{30}^{o}}\]and \[\angle PAC={{30}^{o}},\]meeting XY at B and C respectively.
  A)
  \[(i)\to (ii)\to (iii)\]            done clear
  B)
  \[(iii)\to (ii)\to (i)\] done clear
  C)
         \[(ii)\to (i)\to (iii)\]  done clear
  D)
         \[(iii)\to (i)\to (ii)\] done clear
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