NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry.

Board	CBSE
Textbook	NCERT
Class	Class 8
Subject	Maths
Chapter	Chapter 4
Chapter Name	Practical Geometry
Exercise	Ex 4.1, Ex 4.2, Ex 4.3, Ex 4.4, Ex 4.5
Number of Questions Solved	8
Category	NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

Chapter 4 Practical Geometry Exercise 4.1

Question 1.
Construct the following quadrilaterals:
(i) Quadrilateral ABCD
AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm

(ii) Quadrilateral JUMP
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) First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown.
We may divide it into two conveniently constructible As ABC and ACD.
Steps of Construction :

• Draw AC = 7 cm.
• With A as centre and radius 4.5 cm, draw an arc (below AC).
• With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.
• Join AB and BC.
• With A as centre and radius 6 cm, draw an arc (above AC).
• With C as centre and radius 4 cm, draw another arc cutting the previous arc at D.
• Join AD and CD.
  Then, ABCD is the required quadrilateral.

(ii) First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.
We may divide it into two conveniently constructible As PJU and PMU.
Steps of Construction :

• Draw PU = 6.5 cm.
• With P as centre and radius 4.5 cm, draw an arc (below PU).
• With U as centre and radius 3.5 cm, draw another arc cutting the previous arc at J.
• Join PJ and JU.
• With P as centre and radius 5 cm, draw an arc (above PU).
• With U as centre and radius 4 cm, draw another me cutting the previous arc at M.
• Join PM and UM.
  Then, JUMP is the required quadrilateral.

(iii) Draw a rough sketch of the’ required parallelogram and write down the given dimensions.
Steps of Construction :

• Draw OR = 6 cm.
• With O as centre and radius 7.5 cm, draw an arc.
• With R as centre and radius 4.5 cm, draw another arc to cut the previous arc at E.
• Join OE and RE.
• With 0 as centre and radius 4 5 cm 4.5 cm, draw an arc.
• With E as centre and radius 6 cm, draw another arc to cut the previous arc at M.
• Join MO and ME.
  Then, MORE is the required parallelogram.

(iv) Draw a rough sketch of the required rhombus and write down the given dimensions.
Steps of Construction :

• Draw BE = 4.5 cm.
• With B as centre and radius 4.5 cm, draw an arc. 4 5 cm
• With E as centre and radius 6 cm, draw another arc to cut the previous arc at T.
• Join ST and ET.
• With T as centre and radius 4.5 cm, draw an arc.
• With E as centre and radius 4.5 cm, draw another arc to cut the previous arc at S.
• Join TS and ES.
  Then, BEST is the required rhombus.

Chapter 4 Practical Geometry Exercise 4.2

Question 1.
Construct the following quadrilaterals:
(i) Quadrilateral LIFT
LI = 4 cm
IF = 3 cm
TL = 2.5 cm
LF = 4.5 cm
IT = 4 cm

(ii) Quadrilateral GOLD
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) Let us draw a rough sketch of the required quadrilateral and write down the dimensions. Clearly, the two easily constructible triangles are UT and LIF.
Steps of Construction :

• Draw LI = 4 cm.
• With L as centre and radius 2.5 cm, draw an arc.
• With I as centre and radius 4 cm draw another arc to cut the previous arc at T.
• Join TL and 77.
• With L as centre and radius 4.5 cm, draw an arc.
• With I as centre and radius 3 cm, draw another arc to cut the previously drawn arc at F.
• Join FI, FL and TF.
  Then, LIFT is the required quadrilateral.

(ii) Let us draw a rough sketch of the required quadrilateral and write down its dimensions. Clearly, the two easily constructible triangles are LOD and LGD.
Steps of Construction :

• Draw LD = 5 cm.
• With L as centre and radius 7.5 cm, draw an arc.
• With D as centre and radius 10 cm, draw another arc to cut the previous arc at O.
• Join OL and OD.
• With L as centre and radius 6 cm, draw an arc.
• With D as centre and radius 6 cm, draw an arc to cut the previously drawn arc at B.
• Join GD, GL and OG.
  Then, GOLD is the required quadrilateral.

(iii) We know that the diagonals of a rhombus bisect each other at right angles. So, we proceed according to the following steps.
Steps of Construction :

• Draw BN = 5.6 cm.
• Draw the right bisector XY of BN, meeting BN at O.
• From O set off OE = (6.5) cm = 3.25 cm along OY and OD = 3.25 cm along OX.
• Join BE, EN, ND and DB.
  Then, BEND is the required rhombus.

Chapter 4 Practical Geometry Exercise 4.3

Question 1.
Construct the following quadrilaterals :
(i) Quadrilateral MORE
MO = 6 cm
OR = 4.5 cm
∠M = 60°
∠O = 105°
∠R = 105°

(ii) Quadrilateral PLAN
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) Draw a rough sketch of the required quadrilateral and write down its dimensions.
Steps of Construction :

• Draw MO = 6 cm.
• Make ∠MOX = 105°.
• With O as centre and radius 4.5 cm, cut off OR = 4.5 cm along OX.
• Make ∠ORY = 105°.
• Make ∠ZMO = 60° such that arms RY and MZ intersect at E.
  Then, MORE is the required quadrilateral.

(ii) Draw a rough sketch of the required quadrilateral PLAN and write down its dimensions.
Before taking up the construction let us find the ∠PLA which is equal to 360° – (90°+ 110°+ 85°)
= 360°-285° = 75°.
Steps of Construction :

• Draw PL = 4 cm.
• Make ∠XPL =90°.
• Make ∠YLP = 75°.
• With L as centre and radius 6.5 cm, cut off LA – 6.5 cm along LY.
• Make ∠ZAL =110° and let its arm AZ intersect PX at N.
  Then, PLAN is the required quadrilateral.

(iii) We know that the opposite angles of a parallelogram are equal. Make a rough sketch of the required parallelogram as shown.
Steps of Construction :

• Draw HE = 5 cm.
• Make ∠HEX = 85°.
• With E as centre and radius 6 cm, cut off EA = 6 cm along EX.
• With A as centre and radius 5 cm, draw an arc.
• With H as centre and radius 6 cm, draw another arc cutting the previous arc at R.
• Join HR and AR.
  Then, HEAR is the required parallelogram.

(iv) We known that the opposite sides of a rectangle are equal and each angle of it is 90°.
Make a rough sketch of the required
rectangle and write down its dimensions.
Steps of Construction :

• Draw OK = 7 cm.
• Draw ∠OKX = 90°.
• With K as centre and radius 5 cm, draw an arc KX at A.
• With A as centre and radius 7 cm, draw an arc.
• With O as centre and radius 5 cm, draw another arc cutting the previous arc at Y.
• Join AY and OY.
  Then, OKAY is the required rectangle.

Chapter 4 Practical Geometry Exercise 4.4

Question 1.
Construct the following quadrilaterals:
(i) Quadrilateral DEAR
DE = 4 cm
EA = 5 cm
AR = 4.5 cm
∠E = 60°
∠A = 90°

(ii) Quadrilateral TRUE
TR = 3.5 cm
RU = 3 cm
UE = 4 cm
∠R = 75°
∠U= 120°
Solution.
(i) Let us draw a rough sketch of the required quadrilateral and write down the given dimensions.
Steps of Construction :

• Draw EA = 5 cm.
• Make ∠XEA = 60°.
• With E as centre and radius 4 cm, cut off ED = 4 cm along EX.
• Make ∠EAY = 90°.
• With A as centre and radius 4.5 cm, draw an arc to cut off AY at R.
• Join DR.
  Then, DEAR is the required quadrilateral.

(ii) Let us draw a rough sketch of the required quadrilateral and write down the given 3 5 cm dimensions.
Steps of Construction :

• Draw RU = 3 cm.
• Make ∠URX = 75°.
• With R as centre and radius 3.5 cm, cut off RT = 3.5 cm along RX.
• Make ∠RUY =120°
• With U as centre and radius 4 cm, draw an arc to cut CY at E Join TE.
• Then, TRUE is the required quadrilateral.

Chapter 4 Practical Geometry Exercise 4.5

Question 1.
Draw the following:
Solution.
Draw a rough sketch of the required square and write down its dimensions.
Steps of Construction :

• Draw RE = 5.1 cm.
• DrawRX ⊥RE.
• With R as centre and radius 5.1 cm, draw an arc to cut RX at D.
  
• With D as centre and radius 5.1 cm, draw an arc.
• With E as centre and radius 5.1 cm, draw another arc cutting the previous arc at A.
• Join DA and EA.
  Then, READ is the required square.

Question 2.
A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
Solution:
Let diagonal AC = 5.2 cm and diagonal BD = 6.4 cm.
Draw AC = 5.2 cm. Draw XY, the perpendicular bisector of AC which cuts AC at 0.
With O as centre, draw arcs of radii which
cut OX at D and OY at B.
Join AB, BC, CD and DA.
Then, ABCD is the required rhombus.

Question 3.
A rectangle with adjacent sides of lengths 5 cm and 4 cm.
Solution:
We know that the opposite sides of a Y rectangle are equal and each angle of it is 90°.
Make a rough sketch of the required rectangle and write down its dimensions.
Steps of Construction :

• Draw OK = 5 cm. 5cm
• Draw ∠OKX = 90°.
• With K as centre and radius 4 cm, draw an arc KX at A.
• With A as centre and radius 5 cm, draw an arc.
  
• With O as centre and radius 4 cm, draw another arc cutting the previous arc at Y.
• Join AY and OY.
  Then, OKAY is the required rectangle.

Question 4.
A parallelogram OKAY where OK = 5.5 cm and KA = 42 cm.
Solution:
In order to draw a quadrilateral, we need five measurements.
But here to draw the parallelogram OKAY, we are given two consecutive sides, i.e., four sides (the opposite sides being equal). So, we need information about one of its elements more. It may be the included angle between the sides or one of the diagonals to construct a unique quadrilateral. So, the required parallelogram cannot be drawn.

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