RoboCompass Resources

Learn how to use RoboCompass for Constructions (Playlist)
https://www.youtube.com/playlist?list=PL7_xk_exfNwv01RFRmEf12TAE2i-HMSfC

CLASS-VI : PRACTICAL GEOMETRY

Construction to draw Perpendicular to a line through a point on it
https://www.robocompass.com/share?id=1iuvfnymu65o0
Steps of Constructions:
Step 1 : Draw a line segment AB. Mark point P on AB
Step 2 : With P as centre and a convenient radius, construct an arc intersecting the line segment AB at two points C and D.
Step 3 : With C and D as centres and a radius greater than CP construct two arcs, which cut each other at Q.
Step 4 : Join PQ. Then PQ is perpendicular to AB.
We write PQ ⊥ AB.

Construction to draw Perpendicular to a line through a point not on it
https://www.robocompass.com/share?id=t49ko0xzy1br
Steps of Constructions:
Step 1 : Draw a line segment PQ. Mark point M outside PQ.
Step 2 : With M as centre and a convenient radius, construct an arc intersecting the line segment PQ at two points C and D.
Step 3 : With C and D as centres and a radius greater than half of CD construct two arcs on opposite side of point M, which cut each other at A.
Step 4 : Join AM. Then MA is perpendicular to PQ.
We write MA ⊥ PQ.

NCERT Exercise 14.4
Q1 – https://www.robocompass.com/share?id=1hroqqd65tcmw
Steps of Constructions:
Step 1 : Draw a line segment AB. Mark point M on AB
Step 2 : With M as centre and a convenient radius, construct an arc intersecting the line segment AB at two points C and D.
Step 3 : With C and D as centres and a radius greater than CM construct two arcs, which cut each other at P.
Step 4 : Join PM. Then PM is perpendicular to AB.
We write PM ⊥ AB.

Q2 – https://www.robocompass.com/share?id=1jeaf44uhqqet
Steps of Constructions:
Step 1 : Draw a line segment PQ. Mark point R outside PQ.
Step 2 : With R as centre and a convenient radius, construct an arc intersecting the line segment PQ at two points C and D.
Step 3 : With C and D as centres and a radius greater than half of CD construct two arcs on opposite side of point R, which cut each other at S.
Step 4 : Join RS. Then RS is perpendicular to PQ.
We write RS ⊥ PQ.

Q3 – https://www.robocompass.com/share?id=1hv8ruq61dquq
Steps of Constructions:
Step 1 : Draw a line segment AB. Mark point X on AB
Step 2 : With X as centre and a convenient radius, construct an arc intersecting the line segment AB at two points C and D.
Step 3 : With C and D as centres and a radius greater than CX construct two arcs, which cut each other at Y.
Step 4 : Join XY. Then XY is perpendicular to AB.
Step 5 : With Y as centre and a convenient radius, construct an arc intersecting the line segment XY at two points E and F.
Step 6 : With E and F as centres and a radius greater than half of EF construct two arcs, which cut each other at P.
Step 7 : Join PY. Then PY is perpendicular to XY.

To construct a perpendicular bisector of a line segment
https://www.robocompass.com/share?id=sohe16zyl0z7
Steps of Constructions:
Step 1 : Draw a line segment AB of any length.
Step 2 : With A as centre, using compasses, draw an arc on both sides of AB such that the radius of an arc should be more than half the length of AB.
Step 3 : With the same radius and with B as centre, draw another arc on both sides of AB using compasses. Let it intersect the previous arc at C and D.
Step 4 : Join CD. It intersects AB at O. Therefore, CD is the perpendicular bisector of AB.

NCERT Exercise 14.5
Q1 –http://www.robocompass.com/share?id=1h7fuvrxhw7z8
Steps of Constructions:
Step 1 : Draw a line segment AB of any length.
Step 2 : With A as centre, using compasses, draw an arc on both sides of AB such that the radius of an arc should be more than half the length of AB.
Step 3 : With the same radius and with B as centre, draw another arc on both sides using compasses. Let it intersect the previous arc at C and D.
Step 4 : Join CD. It intersects AB at O. Therefore, CD is the required axis of symmetry of AB.

Q2 – https://www.robocompass.com/share?id=uvjpbuczkx9h
Steps of Constructions:
Step 1 : Draw a line segment PQ = 9.5cm of any length.
Step 2 : With P as centre, using compasses, draw an arc on both sides of PQ such that the radius of an arc should be more than half the length of PQ.
Step 3 : With the same radius and with Q as centre, draw another arc on both sides using compasses. Let it intersect the previous arc at C and D.
Step 4 : Join CD. It intersects PQ at O. Therefore, CD is the perpendicular bisector of PQ.

Q3 – https://www.robocompass.com/share?id=u7zo971801mc
Steps of Constructions:
Step 1 : Draw a line segment XY = 10.3 cm of any length.
Step 2 :  With X as centre, using compasses, draw an arc on both sides of XY such that the radius of an arc should be more than half the length of XY.
Step 3 : With the same radius and with Y as centre, draw another arc on both the sides using compasses. Let it intersect the previous arc at C and D.
Step 4 : Join CD. It intersects XY at M. Therefore, CD is the perpendicular bisector of XY.
Step 5 : Take a point P on extended CD and measure PX and PY
Step 6 : We found that PX = PY
Step 7 : Measure XY and MX. We found that MX = ½ XY

Q4 – https://www.robocompass.com/share?id=ubrgfs5lzk1d
Steps of Constructions:
Step 1 : Draw a line segment AB = 12.8 cm of any length.
Step 2 : With A and B as centres, using compasses, draw arcs on the both sides of AB such that the radius of the arc should be more than half the length of AB. Both will intersect at C and D.
Step 3 : Join CD. It intersects AB at O. Therefore, CD is the perpendicular bisector of AB.
Step 4 : With A and O as centres, using compasses, draw arcs on the same side such that the radius of the arc should be more than half the length of AO. Both will intersect at E and F.
Step 5 : Join EF. It intersects AB at M. Therefore, EF is the perpendicular bisector of AO.
Step 6 : With O and B as centres, using compasses, draw arcs on the same side such that the radius of the arc should be more than half the length of OB. Both will intersect at G and H.
Step 7 : Join GH. It intersects AB at N. Therefore, GH is the perpendicular bisector of OB.
Step 8 : Therefore, AM = MO = ON = NB i.e. AB is divided into four equal parts. 

Q5 – https://www.robocompass.com/share?id=vf1fuitzmpfa
Steps of Constructions:
Step 1 : Draw a line segment AB = 6.1 cm of any length.
Step 2 : With A and B as centres, using compasses, draw arcs on the both sides of AB such that the radius of the arc should be more than half the length of AB. Both will intersect at C and D.
Step 3 : Join CD. It intersects AB at O. Therefore, CD is the perpendicular bisector of AB.
Step 4 : With O as centre and radius OB, draw a circle.

Q6 – https://www.robocompass.com/share?id=1hrbfchgvbs69
Steps of Constructions:
Step 1 : Draw a circle with centre C and radius 3.4 cm.
Step 2 : Draw any chord AB.
Step 3 : With A and B as centres, using compasses, draw arcs on the both sides of AB such that the radius of the arc should be more than half the length of AB. Both will intersect at M and N.
Step 4 : Join MN. It passes through C. 

Q7 – https://www.robocompass.com/share?id=qhkli5jidwl1
Steps of Constructions:
Step 1 : Draw a circle with centre C and radius 3.4 cm.
Step 2 : Draw any diameter AB.
Step 3 : With A and B as centres, using compasses, draw arcs on the both sides of AB such that the radius of the arc should be more than half the length of AB. Both will intersect at M and N.
Step 4 : Join MN. It passes through C. 

Q8 – https://www.robocompass.com/share?id=1hbg1152benvo
Steps of Constructions:
Step 1 : Draw a circle with centre C and radius 4 cm.
Step 2 : Draw any chord AB.
Step 3 : With A and B as centres, using compasses, draw arcs on the both sides of AB such that the radius of the arc should be more than half the length of AB. Both will intersect at M and N.
Step 4 : Join MN.  
Step 5 : Draw any other chord PQ.
Step 6 : With P and Q as centres, using compasses, draw arcs on both sides of PQ such that the radius of the arc should be more than half the length of PQ. Both will intersect at E and F.
Step 7 : Join EF. We observe that MN and EF intersect at centre C.  

Q9 – http://www.robocompass.com/share?id=trrbffnpicm9
Step 1 : Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB.
Step 2 : With O and B as centres, using compasses, draw arcs on the both sides of OB such that the radius of the arc should be more than half the length of OB. Both will intersect at M and N.
Step 3 : Join MN. 
Step 4 : With O and A as centres, using compasses, draw arcs on both sides of OA such that the radius of the arc should be more than half the length of OA. Both will intersect at C and D. 
Step 5 : Join CD intersecting MN at point P.
Step 6 : Measure PA and PB. We observe that PA = PB

Construction of Bisector of an angle
https://www.robocompass.com/share?id=u87zl2ffayic
Steps of Constructions:
Step 1 : Draw an angle ∠COP = 70⁰
Step 2 : With centre O, draw a convenient arc which intersect OP at A and OC at B.
Step 3 : With centre A and B, draw arcs of radius more than half of AB which intersect at D.
Step 4 : Join OD and OD is the required bisector of ∠COP

Constructing a 60° angle
https://www.robocompass.com/share?id=1jetbjfswsqjp
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersect OB at C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : Join OD and ∠DOB = 60⁰

Constructing a 30° angle
https://www.robocompass.com/share?id=qxir7apq7x2w
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersect OB at C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : Join OD and ∠DOB = 60⁰
Step 5 : With centre C and D, draw arcs of radius more than half of CD which intersect at M.
Step 6 : Join OM and ∠MOB = 30⁰

Constructing a 15° angle
https://www.robocompass.com/share?id=1huzyzjat0w2u
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersect OB at C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : Join OD and ∠DOB = 60⁰
Step 5 : With centre C and D, draw arcs of radius more than half of CD which intersect at M.
Step 6 : Join OM intersecting the first arc at P and angle MOB = 30⁰
Step 7 : With centre C and P, draw arcs of radius more than half of CP which intersect at N.
Step 8 : Join ON and ∠NOB = 15⁰

Constructing a 120° angle
https://www.robocompass.com/share?id=t4f29p0g243d
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersect OB at C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : Join OE and ∠EOB = 60⁰

Constructing a 90° angle
https://www.robocompass.com/share?id=1iyfhhlbmmek0
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersect OB at C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : With centres D and E, draw arcs such that the radius is more than half of DE which intersect at M.
Step 6 : Join OM and ∠MOB = 90⁰

Constructing a 45° angle
https://www.robocompass.com/share?id=skv3geng4zea
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersect OB at C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : With centres D and E, draw arcs such that the radius is more than half of DE which intersect at M.
Step 6 : Join OM intersecting the semicircular arc at P.
Step 7 : With centres C and P, draw arcs such that the radius is more than half of CP which intersect at N.
Step 8 : Join ON and ∠NOB = 45⁰

Constructing a 135° angle
https://www.robocompass.com/share?id=t8fpyic7ssvl
Steps of Constructions:
Step 1 : Draw a line and mark O and B.
Step 2 : With centre O, draw a convenient semicircular arc which intersect line at R and C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : With centres D and E, draw arcs such that the radius is more than half of DE which intersect at M.
Step 6 : Join OM intersecting the semicircular arc at P.
Step 7 : With centres R and P, draw arcs such that the radius is more than half of RP which intersect at N.
Step 8 : Join ON and ∠NOB = 135⁰

NCERT Exercise 14.6
Q1. https://www.robocompass.com/share?id=1k1rpkvccnxi9
Steps of Constructions:
Step 1 : Draw an angle ∠COP = 75⁰
Step 2 : With centre O, draw a convenient arc which intersect OP at A and OC at B.
Step 3 : With centre A and B, draw arcs of radius more than half of AB which intersect at D.
Step 4 : Join OD and OD is the required bisector of ∠COP

Q2. https://www.robocompass.com/share?id=qhiavmhttp2p
Steps of Constructions:
Step 1 : Draw an angle ∠COP = 137⁰
Step 2 : With centre O, draw a convenient arc which intersect OP at A and OC at B.
Step 3 : With centre A and B, draw arcs of radius more than half of AB which intersect at D.
Step 4 : Join OD and OD is the required bisector of ∠COP

Q3.https://www.robocompass.com/share?id=to2apby3ks3a
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersects OB at C
Step 3 : With centre C and the same radius, draw an arc which intersects the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : With centres D and E, draw arcs such that the radius is more than half of DE which intersect at M.
Step 6 : Join OM intersecting the semicircular arc at P.  ∠MOB is the required right angle.
Step 7 : With centres C and P, draw arcs such that the radius is more than half of CP which intersect at N.
Step 8 : Join ON and ON is the bisector of the right angle ∠MOB

Q4.https://www.robocompass.com/share?id=u8dysn3eibeb
Steps of Constructions:
Step 1 : Draw an angle ∠COP = 153⁰
Step 2 : With centre O, draw a convenient arc which intersect OP at A and OC at B.
Step 3 : With centre A and B, draw arcs of radius more than half of AB which intersect at D.
Step 4 : Join OD intersecting the first arc at E and OD is the required bisector of ∠COP
Step 5 : With centre B and E, draw arcs of radius more than half of BE which intersect at M.
Step 6 : Join OM and OM is the required bisector of ∠COD
Step 7 : With centre A and E, draw arcs of radius more than half of AE which intersect at N.
Step 8 : Join ON and ON is the required bisector of ∠DOP
Step 9 : Measure ∠COM, ∠DOM, ∠DON and ∠NOP. All angles are of equal measure and hence 153⁰ is divided into four equal parts.
Q6.https://www.robocompass.com/share?id=s4xdclqcasti
Steps of Constructions:
Step 1 : Draw a line segment OB.
Step 2 : With centre O, draw a convenient arc which intersects OB at C
Step 3 : With centre C and the same radius, draw an arc which intersects the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : With centres D and E, draw arcs such that the radius is more than half of DE which intersect at M.
Step 6 : Join OM intersecting the semicircular arc at P and ∠MOB = 90⁰
Step 7 : With centres C and P, draw arcs such that the radius is more than half of CP which intersect at N.
Step 8 : Join ON intersecting the semicircular arc at A and ∠NOB = 45⁰
Step 9 : With centres C and R, draw arcs such that the radius is more than half of CR which intersect at A.
Step 10 : Join OA and ∠AOB = 22½5⁰

Q7.https://www.robocompass.com/share?id=sok35bvkf6t3
Steps of Constructions:
Step 1 : Draw a line and mark O and B.
Step 2 : With centre O, draw a convenient semicircular arc which intersect line at R and C
Step 3 : With centre C and same radius, draw an arc which intersect the previous arc at D.
Step 4 : With centre D and same radius, draw another arc which intersect the first arc at E.
Step 5 : With centres D and E, draw arcs such that the radius is more than half of DE which intersect at M.
Step 6 : Join OM intersecting the semicircular arc at P.
Step 7 : With centres R and P, draw arcs such that the radius is more than half of RP which intersect at N.
Step 8 : Join ON intersecting the semicircular arc at Q and ∠NOB = 135⁰
Step 9 : With centres Q and C, draw arcs such that the radius is more than half of QC which intersect at A.
Step 10 : Join OA and OA is the bisector of angle 135⁰.

Q8.https://www.robocompass.com/share?id=1jeo958t0tauu
Steps of Constructions:
Step 1 : Draw an angle ∠COP = 70⁰
Step 2 : Draw a line segment AB
Step 3 : With centre O, draw a convenient arc which intersect OP at M and OC at N.
Step 4 : With centre A, draw the arc of same radius OM which intersect AB at D.
Step 5 : Measure arc MN
Step 6 : With centre D, draw an arc of radius MN which intersect the arc at E
Step 7 : Join AE and ∠EAB = 70⁰

Q9.https://www.robocompass.com/share?id=1iyl0btg7uvch
Steps of Constructions:
Step 1 : Draw an angle ∠COP = 40⁰ and extend PO.
Step 2 : Draw a line segment AB
Step 3 : With centre O, draw a convenient arc which intersects extended PO at M and OC at N.
Step 4 : With centre A, draw the arc of same radius OM which intersect AB at D.
Step 5 : Measure arc MN
Step 6 : With centre D, draw an arc of radius MN which intersect the arc at E
Step 7 : Join AE and ∠EAB = 140⁰

CLASS-IX : CONSTRUCTIONS

To construct Perpendicular bisector of a given line segment
https://www.robocompass.com/share?id=t89nozlizpkl

To construct the bisector of a given angle.
http://www.robocompass.com/share?id=s18ekpl7jcxk

To construct an angle of 60 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1iuvgd69lx645

To construct an angle of 30 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1hrgyidz0ymuv

To construct an angle of 90 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1ib3p3cwxda9h

To construct an angle of 15 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=qe12e42k6gjd

To construct an angle of 45 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1iv6ior995rn5

To construct an angle of 22.5 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=rhlodtzco3tx

To construct an angle of 75 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1jygkd47ezpkk

To construct an angle of 105 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1hbazeud5omk5

To construct an angle of 135 degree at the initial point of a given ray.
http://www.robocompass.com/share?id=1hb86xl18qn36

To construct an equilateral triangle, given its side
http://www.robocompass.com/share?id=veynofye0yep

To construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13 cm.
http://www.robocompass.com/share?id=1jew25g4srsj7

To construct a triangle ABC in which BC = 8cm, ∠B = 45° and AB – AC = 3.5 cm.
http://www.robocompass.com/share?id=1iv9vimugcz05

To construct a triangle PQR in which QR = 6cm, ∠Q = 60° and PR – PQ = 2cm.
http://www.robocompass.com/share?id=1jed7a80z4h29

To construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.
http://www.robocompass.com/share?id=vb6d4hpnrn07

To construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18 cm.
http://www.robocompass.com/share?id=t4a1cnw350l0

CLASS-X : CONSTRUCTIONS

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts
http://www.robocompass.com/share?id=1iuw08wrxskmc

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it, whose sides are 2/3 of the corresponding sides of the first triangle.
http://www.robocompass.com/share?id=1jew2589i8xgl

Construct a triangle of sides 5 cm, 6 cm and 7 cm and then a triangle similar to it, whose sides are 7/5 of the corresponding sides of the first triangle.
http://www.robocompass.com/share?id=soccsk097ghf

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the sides of the isosceles triangle.
http://www.robocompass.com/share?id=qe4dndqrnvhw

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.
http://www.robocompass.com/share?id=s4ulktiz5ely

Draw a triangle ABC with side BC = 7 cm, ∠ B = 45°, ∠ A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of Δ ABC.
http://www.robocompass.com/share?id=1jxzf36oavqk4

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
http://www.robocompass.com/share?id=1hruuxtj8dxrn

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
http://www.robocompass.com/share?id=vf1fukfh8x15

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
http://www.robocompass.com/share?id=sonfw2xqdg6v

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
http://www.robocompass.com/share?id=1h84ss561ag6c

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.
http://www.robocompass.com/share?id=1iv3t9dz3fh44

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
http://www.robocompass.com/share?id=1h7zs09kqrcqh

Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
http://www.robocompass.com/share?id=u8b84fsm7q75

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
http://www.robocompass.com/share?id=ubp69wk1u721