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 1 :

**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 1 :

**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 1 :

**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 1 :

**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 1 :

**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 1 :

**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 1 :

**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 1 :

**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