Lesson: Practical Geometry
Exercise 4.1
Question 1
AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm, AC = 7 cm.
JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm.
(iii) Parallelogram MORE
OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm.
(iv) Rhombus BEST:
BE = 4.5 cm, ET = 6 cm.
Solution:
(i) Steps of construction:
1. Draw a line segment AC = 7 cm.
2. Draw an arc of radius AB = 4.5 cm taking A as centre.
3. Draw another arc of radius 5.5 cm taking C as centre on the same side of
AC in which the earlier arc was drawn.
4. Let these two arcs intersect at B.
5. Join AB and CB to obtain ABC.
6. Similarly, draw ADC on the other side of AC taking = 6 cm and DC = 4
cm.
7. ABCD is the required quadrilateral.
(ii) Steps of construction:
1. Draw a line segment PU = 6.5 cm.
2. Taking P as centre draw an arc of radius 4.5 cm.
3. Taking U as centre draw another arc of radius 3.5 cm on the same side of
PU in which the earlier arc was drawn.
4. Let these two arcs intersect at J.
5. Join PJ and UJ.
6. Similarly, obtain the point M on the opposite side of diagonal PU, where
PM= 5 cm and MU = 4 cm.
7. JUMP is the required quadrilateral.
(iii) Steps of construction:
1. Draw a line segment EO = 7.5 cm.
2. Taking E as centre draw an arc of radius 6 cm.
3. Taking O as centre draw another arc of radius 4.5 cm
on the same side of EO in which the earlier arc was drawn.
4. Let the point of intersection of these two arcs be M.
5. Join EM and MO.
6. We get the EMO.
7. Similarly, obtain EOR with arc lengths ER = 4.5 cm and OR = 6 cm
on the other side of EO.
8. MORE is the required parallelogram.
(iv) Steps of construction:
1. Draw ET = 6 cm.
2. Draw two arcs of radius 4.5 cm taking E and T as centre on the same side
of ET.
3. Let these two arcs meet at B. Join EB and TB.
4. Similarly, on the opposite side of ET draw triangle EST by taking
ES = TS = 4.5 cm.
5. BEST is the required rhombus.
Exercise 4.2
Question 1
LI = 4 cm, IF = 3 cm, TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm,
OL = 7.5 cm, GL = 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm
(iii) Rhombus BEND
BN = 5.6 cm, DE = 6.5 cm
Solution:
(i) Steps of construction:
1. Draw a line segment LI = 4 cm.
2. With L and I as centers and radii of 2.5 cm and 4 cm
respectively draw two arcs intersecting at T.
3. Join TL and TI.
4. Again with L and I as centers and radii of 4.5 cm and
3cm respectively draw two arcs intersecting at F.
5. Join FL, TF and FI.
6. LIFT is the required quadrilateral.
(ii) Steps of construction:
1. Draw a line segment OL = 7.5 cm.
2. With O and L as centers and radii 10 cm and 5 cm
respectively draw two arcs intersecting at D.
3. Join OD and LD.
4. Again with L and D as centers and radii 6 cm, draw
two arcs intersecting each other at G.
5. Join GD, GO and LG.
6. GOLD is the required quadrilateral.
(iii) Steps of construction:
1. Draw a line segment DE = 6.5 cm.
2. Draw perpendicular bisector XY of DE which
Intersects DE at O.
3. Taking O as centre draw two arcs of radii 2.8 cm on
opposite sides of DE, which intersects XY at B and N
as shown in figure.
4. Join BD, BE, EN and DN.
5. BEND is the required rhombus.
Exercise 4.3
Question 1
MO = 6 cm, OR = 4.5 cm, M = 60
0
, O = 105°, R = 105°,
PL = 4 cm, LA = 6.5 cm,P = 90°, A = 110°, N = 85°
(iii) Parallelogram HEAR
HE = 5 cm, EA = 6 cm, R = 85°
(iv) Rectangle OKAY
OK = 7 cm, KA = 5 cm
Solution:
(i) Steps of construction:
1. Draw a line segment MO = 6 cm.
2. At O, draw an XOR = 105° .
3. From ray OX, cut OM = 6 cm.
4. At R, draw an ORY = 105° .
5. At M, draw OMZ = 60°, the rays RY and MZ
intersect each other at E.
6. MORE is the required quadrilateral.
(ii) Steps of construction:
1. Draw a line segment AL = 6.5 cm.
2. At A, draw an XAL = 110°.
3. At L, draw an angle YLA = 75°.
4. Taking L as centre draw an arc of radius 4 cm, which
will intersects LY at P.
5. At P draw angle LPN = 90°. Ray AX and arm PN of
angle LPN intersect at N.
6. PNA = 85°, because remaining three angles add up
to 275°.
7. PLAN is the required quadrilateral.
(iii) Steps of construction:
1. Draw a line segment HE = 5 cm.
2. At E, draw HEX= 85° and cut off EA = 6 cm from
EX.
3. Here H = 180° 85° = 95°.
4. Now draw EHY = 95° and cut off HR=6 cm from HY.
5. Join HR and RA.
6. HEAR is the required parallelogram.
(iv) Steps of construction:
1. Draw a line segment OK = 7 cm.
2. AT O, draw an XOK = 90°.
3. From ray OX, cut off OY = 5 cm.
4. Also at K, draw an OKZ = 90°.
5. From ray KZ, cut off KA = 5 cm.
6. Join AY.
7. OKAY is the required rectangle.
Exercise 4.4
Question 1
DE = 4 cm, EA = 5 cm, AR = 4.5 cm, E = 60°°, A = 90°
TR = 3.5 cm, RU = 3 cm, UE = 4 cm, R = 75°, U = 120°
Solution:
(i) Steps of construction:
1. Draw a line segment EA = 5 cm.
2. Draw an XEA = 60° and EAY = 90°.
3. Cut off ED = 4 cm from EX and AR = 4.5 cm
from AY.
4. Join DR.
5. DEAR is the required quadrilateral.
(ii) Steps of construction:
1. Draw YRX = 75°.
2. With centre R and radius 3.5 cm draw and arc to
intersect RY in T.
3. With centre R and radius 3 cm draw an arc to intersect
RX in U. Note- In the figure make RU = 3 cm.
4. Draw RUZ = 120°.
5. With centre U and radius 4 cm draw an arc to intersect
UZ in E.
6. Join TE.
7. TRUE is the required quadrilateral.
Exercise 4.5
Question 1
Draw the following:
The square READ with RE = 5.1 cm.
Solution:
Steps of construction:
1. Draw a line segment RE = 5.1 cm.
2. At R, draw angle ERY = 90° and at E, draw angle REX = 90°.
3. Taking E and R as centre draw two arcs of radius 5.1 cm, which
intersect RY and EX at D and A respectively.
5. READ is the required square.
Question 2
Draw the following:
A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
Solution:
Steps of Construction:
1. Show the point Y in the figure.
2. Draw a line segment BD = 5.2 cm.
3. Draw perpendicular bisector XY of BD which intersects BD at O.
4. Now, taking O as centre draw two arcs of radius 3.2 cm on the
opposite sides of BD, which intersect BD at A and C.
5. Join AB, AD, BC and CD.
6. ABCD is the required rhombus.
Question 3
Draw the following:
A rectangle with adjacent sides of lengths 5cm and 4cm.
Solution:
Steps of construction:
1. Draw a line segment AB = 5 cm.
2. Construct BAY = ABX = 90°.
3. Draw arcs of radius 4 cm.
4. Taking A and B as centre,
which intersect AY and BX at D and C respectively.
5. Join DC.
6. ABCD is the required rectangle.
Question 4
Draw the following:
A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?
Solution:
We know that, opposite sides of a parallelogram are equal and sum of