# NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry  Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 8 Maths Chapter 4 Practical Geometry Exercise 4.1

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

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

(i) Draw a rough sketch first as per the given dimensions. Construction:
Step 1: Draw a line segment AB = 4.5 cm

Step 2: Draw an arc with center as B and of radius 5.5 cm.

Step 3: Similarly, draw another arc with center as A and radius 7 cm to meet the previous arc at C.

Step 4: Now taking radius 4 cm, draw an arc with centre C and also draw another arc with center A and radius 6 cm to cut the former arc at D.

Step 5: Join BC, AC, CD and AD.

Hence, we have got the required figure as per the given data.

(ii) Draw a rough sketch first as per the given dimensions. Construction:
Step 1: Draw a line segment JU = 3.5 cm.

Step 2: Draw an arc with centre at J and radius 4.5 cm.

Step 3: Draw another arc with centre at U and radius 6.5 cm to meet the previous arc at P and join JP and UP.

Step 4: Now with radius 4 cm, draw an arc with centre at U.

Step 5: Draw another arc with centre P and radius 5 cm to meet the previous arc at M. Step 6: Join UM and PM.

Hence we have, JUMP as the required quadrilateral.
(iii) Draw a rough sketch first as per the given dimensions and we know that opposite sides of a parallelogram are equal. Construction:
Step 1: Draw a line segment OR = 6 cm.
Step 2: Draw an arc with centre at R and of radius 4.5 cm.

Step 3: Draw another arc with centre at O and radius 7.5 cm to meet the previous arc at E and join RE and OE.

Step 4: Draw an arc with centre at E and radius 6 cm.

Step 5: Draw another arc with centre at O and radius 4.5 cm to meet the former arc at M. Step 6: Join EM and OM.

Hence we have, MORE as the required parallelogram with given dimensions.

(iv) Draw a rough sketch first as per the given dimensions and we know that all sides of a rhombus are equal. Construction:

Step 1: Draw BE = 4.5 cm

Step 2: Draw an arc with centre B and radius 4.5 cm.

Step 3: Draw another arc with centre E and radius 6 cm to meet the previous arc at T and join BT and ET.

Step 4: Draw two arcs with centres E and T with equal radii 4.5 cm to meet each other at S and join ES and TS, and join ES and TS.

Hence we have, BEST as the required rhombus with given dimensions.

## NCERT solutions for class 8 Maths Chapter 4 Practical Geometry Exercise 4.2

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

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

(i)Draw a rough sketch first as per the given dimensions. Construction:

Step 1: Draw a line segment LI = 4 cm.

Step 2: Draw an arc with centre at I and radius 3 cm.

Step 3: Draw another arc with centre L and radius 4.5 cm to meet the former arc at F and Join LF and IF.

Step 4: Draw an arc with centre L and radius 2.5 cm.

Step 5: Draw another arc with centre I and radius 4 cm to meet the previous arc at T and Join LT and IT.

Hence we have LIFT as the required quadrilateral with given dimensions.

(ii)Draw a rough sketch first as per the given dimensions. Construction:

Step 1: Draw a line segment OL = 7.5 cm

Step 2: Draw an arc with centre at O and of radius 10 cm.

Step 3: Draw another arc with centre at L and of radius 5 cm to meet the previous arc at D and join OD and LD.

Step 4: Draw an arc with centre L and D with equal radii of 6 cm to meet each other at G and join LG and DG.

Hence we have GOLD as the required quadrilateral with given dimensions.

(iii)Draw a rough sketch first as per the given dimensions and we know that the diagonals of a rhombus bisect each other at the right angle. Construction:

Step 1: Draw a line segment BN = 5.6 cm.

Step 2: Draw the right bisector of BN at O.

Step 3: Draw two arcs with centre O and radius $$\frac { 1 }{ 2 } \times DE$$, i.e., $$\frac { 1 }{ 2 } \times 6.5 = 3.25 cm$$ to meet the right bisector at D and E.

Step 4: Join BE, EN, ND and BD.

Hence we have, BEND as the required rhombus with given dimensions.

## NCERT solutions for class 8 Maths Chapter 4 Practical Geometry Exercise 4.3

MO = 6 cm ∠R = $$105^{\circ}$$, OR = 4.5 cm, ∠M = $$60^{\circ}$$, ∠O = $$105^{\circ}$$

PL = 4 cm, LA = 6.5 cm, ∠P = $$90^{\circ}$$, ∠A = $$110^{\circ}$$, ∠N = $$85^{\circ}$$

(iii) Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = $$85^{\circ}$$

(iv) Rectangle OKAY

OK = 7 cm, KA = 5 cm

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

(i) Draw a rough sketch first as per the given dimensions. Construction:

Step 1: Draw a line segment OR = 4.5 cm

Step 2: Draw an angle of $$105^{\circ}$$ at O and also an angle of $$105^{\circ}$$ at R with the help of protractor.

Step 3: Make an arc OM = 6 cm.

Step 4: Draw an angle of $$60^{\circ}$$ at M to meet the line through R at E.

Hence we have, MORE as the required quadrilateral.

(ii)Draw a rough sketch first as per the given dimensions. Construction:

Step 1: Draw a line segment LA = 6.5 cm

Step 2: Draw an angle of 75° at L and $$110^{\circ}$$ at A with the help of a protractor. [$$∵ 360^{\circ} – (110^{\circ} + 90^{\circ} + 85^{\circ}) = 75^{\circ}$$]

Step 3: Cut LP = 4 cm.

Step 4: Draw an angle of 90° at P which meets the line through A at N.

Hence we have PLAN as the required quadrilateral.

(iii)Draw a rough sketch first as per the given dimensions and we know that opposite sides of a parallelogram are equal. Construction:

Step 1: Draw a line segment HE = 5 cm.

Step 2: Draw an angle of $$85^{\circ}$$ at E and cut an arc of EA = 6 cm.

Step 3: Draw an arc with centre A and radius 5 cm.

Step 4: Draw another arc with centre H and radius 6 cm to meet the previous arc at R and join HR and AR.

Hence we have, HEAR as the required parallelogram.

(iv)Draw a rough sketch first as per the given dimensions and we know that each angle of a rectangle is $$90^{\circ}$$ and opposite sides are equal. Construction:

Step 1: Draw a line segment OK = 7 cm.

Step 2: Draw the angle of $$90^{\circ}$$ at K and cut an arc of KA = 5 cm.

Step 3: Draw an arc with centre at O and radius 5 cm.

Step 4: Draw another arc with centre at A and radius 7 cm to meet the previous arc at Y and join OY and AY.

Hence we have OKAY as the required rectangle.

## NCERT solutions for class 8 Maths Chapter 4 Practical Geometry Exercise 4.4

DE = 4 cm, EA = 5 cm, AR = 4.5 cm, ∠E = $$60^{\circ}$$, ∠A =$$90^{\circ}$$

TR = 3.5 cm, RU = 3 cm, UE = 4.5 cm, ∠R = $$75^{\circ}$$, ∠U =$$120^{\circ}$$

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

(i)Draw a rough sketch first as per the given dimensions Construction:

Step 1: Draw a line segment DE = 4 cm.

Step 2: Draw an angle of $$60^{\circ}$$ at E.

Step 3: Draw an arc with centre E and radius 5 cm to meet the angle line at A.

Step 4: Draw an angle of $$90^{\circ}$$ at A and cut an arc AR = 4.5 cm and join DR.

Hence we have, DEAR as the required quadrilateral.

(ii)Draw a rough sketch first as per the given dimensions Construction:

Step 1: Draw a line segment TR = 3.5 cm

Step 2: Draw an angle of $$75^{\circ}$$ at R and cut RU = 3 cm.

Step 3: Draw an angle of $$120^{\circ}$$ at U and cut UE = 4.5 cm.

Step 4: Join TE.

Hence we have TRUE as the required quadrilateral.

## NCERT solutions for class 8 Maths Chapter 4 Practical Geometry Exercise 4.5

1.The square READ with RE = 5.1 cm.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

Construction: Step 1: Draw RE = 5.1 cm.

Step 2: Draw an angle of $$90^{\circ}$$ at E and cut an arc EA = 5.1 cm.

Step 3: Draw two arcs from A and R with radius 5.1 cm to cut each other at D.

Step 4: Join RD and AD.

Hence we have, READ as the required square.

2.A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

Construction: Step 1: Draw a line segment AC = 6.4 cm.

Step 2: Draw the right angle bisector of AC at E.

Step 3: Draw two arcs with centre at E and radius = $$\frac { 5.2 }{ 2 }$$ = 2.6 cm to cut the previous diagonal at B and D.

Step 4: Join AD, AB, BC and DC.

Hence we have ABCD as the required rhombus.

3.A rectangle with adjacent sides of lengths 5 cm and 4 cm.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

Construction: Step 1: Draw PQ = 5 cm.

Step 2: Draw an angle of $$90^{\circ}$$ at Q and cut an arc QR = 4 cm.

Step 3: Draw an arc with centre R and radius 5 cm.

Step 4: Draw another arc with centre P and radius 4 cm to meet the previous arc at S.

Step 5: Join RS and PS.

Hence we have PQRS as the required rectangle.

4.A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

Construction: Step 1: Draw a line segment OK = 5.5 cm.

Step 2: Draw an angle of any measure (let's say $$60^{\circ}$$) at K and cut an arc KA = 4.2 cm.

Step 3: Draw an arc with centre A and radius of 5.5 cm.

Step 4: Draw another arc with centre O and radius 4.2 cm to cut the previous arc at Y.

Step 5: Join AY and OY.

Hence we have OKAY as the required parallelogram.

No, it is not a unique parallelogram because the angle at K can be of any measure other than $$60^{\circ}$$.

##### FAQs Related to NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry
There are total 8 questions present in ncert solutions for class 8 maths chapter 4 practical geometry
There are total 3 long question/answers in ncert solutions for class 8 maths chapter 4 practical geometry
There are total 5 exercise present in ncert solutions for class 8 maths chapter 4 practical geometry 