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Constructions - Class 9 Maths - Extra Questions

Construct a scalene triangle ABC, given base AB=3 cm, base angle =90o and sum of the lengths BC+AC=9 cm.



Draw ABC of measure 110 and bisect it.



Construct a bisector of an angle of 60o.



Draw ABC of measure 115 and bisect it.



Construct an angle of 45o using compass.



Draw the following angles using ruler and compasses. Also label them. 
45o



Construct ΔPQR, such that QR=6.5cm, PQR=600 and PQPR=2.5cm.



The construction of ΔPQR given that QR=5.2 cm angle Q=50. Is it possible when the difference of PQ and PR is 3.5 cm? justify.



Draw the following angles using ruler and compasses. Also label them. 
90o



How many of the given letters have perpendicular lines?
MATHS



Draw an angle of measure 45o and bisect it.



Draw a right angle.



Draw POQ of measure 75o and find its line of symmetry.



Draw the following angles using ruler and compasses. Also label them. 
30



Draw a line segment XY=7cm and draw AXY=90



Construct the angle of 30o using a ruler and compass.



Construct an angle of the measure 45 with ruler and compasses.



Construct with ruler and compasses, angle of the following measure:
30^{o}



Construct angles of following measures using ruler and compasses.
90^{o}



What is an angle bisector ?



Construct with ruler and compasses, angle of the following measure:
90^{o}



Construct angles of following measures using ruler and compasses.
60^{o}



Construct a bisector of an angle.



Construct a triangle ABC whose perimeter 12 cm and who base angles are { 50 }^{ \circ  } and { 80 }^{ \circ  }.



Construct with ruler and compasses, angle of following measures.
135^o.



Construct an angle of 45^\circ at the initial point of a given ray OA, using a ruler and compasses.



Construct with ruler and compasses, angle of following measures.
60^o.



Construct with ruler and compasses, angle of following measures.
90^o.



Draw an angle of measure 135^o and bisect it.



Construct with ruler and compasses, angle of following measures.
30^o.



Construct with ruler and compasses, angle of following measures.
120^o.



Draw a right angle and construct its bisector.



Construct with ruler and compasses, angle of following measures.
45^o.



Draw an angle of 45 ^ { \circ } , using a pair of compasses.



In this question, use a straight edge and compasses only and show all your construction arcs. Construct the bisector of angle ABC.

1645275_188f3b059efd47ff9ef44c0095fd3805.png



In this question, use a straight edge and compasses only and show all your construction arcs. Construct the perpendicular bisector of PQ.
1645274_43ad6348f7404801bc842ae874587e10.png



Construct a \triangle ABC in which: AB= 5.4\ cm, \angle CAB= 45^{0} and AC\, +\, BC= 9\ cm.
Then the length of AC (in cm.) is:



Construct a triangle PQR in which \angle Q = 60^o and \angle R = 45^o and PQ + QR + PR = 11\ cm.



Construct a \triangle ABC in which AC= 5\ cm, and \angle BAC= 60^{\circ} and AB\, -\, BC= 1.2\ cm.



Construct the bisector of an angle 75^o.



Construct an angle of 60^o using compass.



Construct a triangle whose perimeter is 9.8\ cm and the base angles are 45^\circ and 60^\circ.



Construct a triangle ABC in which \displaystyle BC=5.6  cm, \displaystyle \angle B=45^{\circ} and \displaystyle AB+AC=8\ cm .



Construct a \triangle PQR, such that \angle Q=70^o, \angle R=70^o and PQ+QR+RP =10 cm.



Construct a triangle ABC in which BC = 6\ cm, \angle A = \displaystyle 45^{\circ} and median AD = 5\ cm.



Construct \triangle MNO such that NO = 6.2\ cm, \angle N = 50^\circ and MO - MN = 2.4\ cm.



Perimeter of \triangle ABC is 14cm, AB=4.5 cm and \angle A = 80^o. Construct \triangle ABC.



Construct an angle of 30^o using compass.



Construct \triangle MNO where base NO = 6.7\ cm, \angle MNO = 45^\circ and MO-MN = 2.8\ cm.



Construct \triangle LMN in which base MN= 7\ cm, \angle LMN=75^\circ and LM+LN = 9\ cm.



Construct a triangle XYZ in which \angle {Y}={30}^{o}, \angle {Z}={90}^{o} and XY+ZX+YZ=11cm.



Construct a triangle ABC in which BC=7cm, \angle {B}={75}^{o} and AB+AD=13\ cm.



Construct \triangle PQR such that perimeter of \triangle PQR is 16\ cm and \angle Q=90^\circ and QR = 5\ cm.



Construct an angle of {90}^{\circ} at the initial point of a given ray and justify the construction.



Construct an equilateral triangle, given its side =3 cm and justify the construction.



Construct a triangle PQR in which QR=6cm, \angle {Q}={60}^{o} and PQ-PO=2cm.



Construct the angles of the following measurements:
(i) {30}^{\circ}
(ii) {22\cfrac{1}{2}}^{\circ}
(iii) {15}^{\circ}



Construct a triangle ABC whose perimeter 12 cm and whose base angles are 65^{\circ} and 85^{\circ}



Construct a triangle ABC whose perimeter 12 cm and whose base angles are 50^{\circ} and 80^{\circ}



Construct triangle ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and \angle B = 45^{\circ}



Construct a triangle ABC, whose perimeter is 12 cm and whose sides are in the ratio 3 : 4 : 5



Construct triangle ABC in which BC = 5 cm, AB - AC = 2.8 cm and \angle B = 40^{\circ}



Construct triangle ABC in which BC = 6 cm, AB - AC = 3.1 cm and \angle B = 30^{\circ}



Construct a triangle ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and \angle B = 60^{\circ}



Construct a triangle ABC in which AB=5.6 cm, BC = 5.4 cm and \angle B = 40^{\circ}



Construct a triangle ABC, whose perimeter is 12 cm and whose sides are in the ratio 2 : 3 : 4.



Construct a triangle XYZ whose perimeter 15\ cm and whose base angles are 60^{\circ} and 70^{\circ}



Draw \angle ABC of measure 120^{\circ} and bisect it.



Construct a triangle ABC in which AB = 5.8\ cm, BC + CA = 8.4\ cm and \angle B = 60^{\circ}



Using a ruler and compass only.
(i) Construct a \triangle ABC with the following data.
AB=3.5\ cm, BC=6\ cm and \angle ABC=120^\circ
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure \angle BCP.



Construct a triangle ABC in which base AB = 5 cm, \angle A = 30^{\circ} and AC - BC = 2.5 cm



Construct a triangle ABC whose perimeter is 12.5 cm and whose base angles are 60^{\circ} and 75^{\circ}



Construct an angle of {45}^{o} and bisect it.



Draw \angle ABC of measure 125^o and bisect it.



Construct a triangle PQR in which QR=5\ cm,\angle R=40^{o} and PR-PQ=1\ cm.



Construct a triangle ABC in which BC=7cm,\angle{B}={75}^{o} and AB+AC=13cm



Construct an angle of {90}^{o} at the initial point of a given ray and justify the construction.



If the measure of an angle is equal to {225}^{\circ}, then find the fraction of one complete turn?



Construct \triangle ABC in which BC=6.3\ cm \angle B=75^{o} and AB+AC=9\ cm.



Construct \triangle XYZ in which \angle Y=30^{o}, \angle Z=60^{o} and XY+YZ+ZX=10\ cm.



Write the steps to construct  \triangle ABC, in which BC=5.2\ cm, \angle ACB={45}^{\circ} and perimeter of \triangle ABC is 10\ cm.



Construct an angle of {45}^{o} at the initial point of a given ray and justify the construction.



Construct \Delta ABC, such that BC = 6cm,\angle ABC = {100^0} and AC - AB = 2.5cm.



Construct  an angle of 45^{\circ} at the initial point of a given point of a given ray and justify the construction.



Construct an angle of 90^{o} at the point of a given ray and justify the construction.



Draw the following angles using ruler and compasses. Also label them. 
60^{o}



Draw the following angles using ruler and compasses. Also label them. 
180^{o}



Draw an angle of measure {147^ \circ } and construct its bisector.



Draw an angle of measure {147}^{\circ} and construct its bisector



Draw a line segment PQ=6.2\ cm. Draw the perpendicular bisector of PQ.
1418160_fb260bd252c943799f6046ee547c7a8e.png



Construct a triangle ABC in which BC=8cm,\angle{B}={45}^{\circ} and AB-AC=3.5cm



Construct a \triangle ABC in which BC=5.6\ cm, \angle B=30^{o} and the difference between the other sides is 3\ cm.



Construct triangle ABC having given BC=7\ cm,\ AB-AC=1\ cm and \angle\ ABC=45^{o}.



Construct a perpendicular line from point p to any line AB.



Use ruler and compasses only for this question.
Construct a \triangle ABC,\,AB=3.5cm,\,BC=6cm,\,\&\,\angle ABC=60^\circ
Mark the point P which is equidistant from AB, BC and also equidistant from B and C.



Construct a triangle ABC in which BC=8cm,\angle B={ 45 }^{ \circ  }andAB-AC=3.5cm. 



Draw an angle of 60^\circ, using a pair of compasses. Bisect it to make an angle of 30^\circ.



Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA=OB. Draw the perpendicular bisectors of \overline{OA} and \overline{OB}. Let them meet at P. Is PA=PB?



Without using set-squares or protractor construct:
Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.



BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If L is the mid-point of BC, prove that LM=LN.



Construct a \Delta ABC in which BC=5 cm, \angle B=45 and AB-AC=2.8cm



ABC is a triangle. D is a point on AB such that AD=\dfrac{1}{4}AB and E is a point on AC such that AE=\dfrac{1}{4}AC. Prove that DE=\dfrac{1}{4}BC.



Draw a right triangle having hypotenuse of length 5.4cm, and one of the acute angles of measure 30^o.



Draw an angle of measure 127^{\circ} and construct its bisector.



Without using set-squares or protractor construct:
construct a \triangle ABC,\,AB=5.5cm,\,BC=3.2cm,\,\&\,AC=4.8cm
Find the locus which is equidistant from sides BC\,\&\,AC and also at a distance of 2.5cm from B
Mark the point of intersection of the loci with the letter P and measure PC.



Bisect the \angle  XYZ and write the steps of construction as well.

1790379_33e286fd41c14cecae0bff8157cda52b.png



Draw a line segment AB=8\ cm. Mark a point P in AB so that AP =5\ cm . At P , construct \angle  APQ=30^\circ.



Construct angle ABC=45^o in which BC=5cm and AB=4.6cm.



Construct an angle of {45}^{\circ} from a horizontal line and justify the construction.



Using a protractor, draw \angle BAC of measure 45^{\circ}. Take a point P in the interior of \angle BAC. From P draw line segments PM and PN such that PM \perp AB and PN \perp AC, Measure \angle MPN.



Construct a  triangle ABC with AB=5.5\ cm,AC=6\ cm and \angle BAX=105^{o}
Hence :
Construct the locus of point equidistant from B and C



In triangle ABC; angle A=90^{o}, side AB=x\ cm,\ AC=(x+5)\ cm and area =150\ cm^{2}. Find the sides of the triangle.



Construct a  triangle ABC with AB=5.5\ cm,AC=6\ cm and \angle BAX=105^{o}
Hence :
Construct the locus of points equidistant from BA and BC .



Construct a \triangle A B C in which B C = 3.6 cm, A B = 5 cm and A C = 5.4 cm. Draw the perpendicular bisector of the side B C.



Construct a triangle XYZ in which \angle Y = {30}^0 , \angle Z = {90}^0 and XY + YZ + ZX = 11 cm .



Draw a triangle ABC in which BC=4cm, AB=3cm and \angle B=45^o. Also, draw a perpendicular from A on BC.



Construct \DeltaABC in which AB=6.4cm, \angle A=45^o and \angle B=60^o.



Construct the following angles with the help of ruler and compasses only:150^{\circ}



Construct the following angles with the help of ruler and compasses only:105^{\circ}



Draw \DeltaABC in which AC=6cm, \angle A=90^o and \angle B=60^o.



Draw \DeltaABC in which \angle C=90^o and AC=BC=4cm.



Using ruler and compasses only, draw a right angle.



Draw \DeltaPQR in which \angle Q=80^o, \angle R=55^o and QR=4.5cm. Draw the perpendicular bisector of side QR.



Draw \DeltaABC in which \angle A=120^o, AC=AB=3cm. Measure \angle B and \angle C.



Class 9 Maths Extra Questions