NCERT Solutions for Class 8 Maths Chapter 4: Practical Geometry

The NCERT Solutions for Class 8 Maths Chapter 4 on Practical Geometry offer valuable assistance to students, facilitating a comprehensive understanding of the subject and aiding them in achieving high marks in examinations. These solutions feature meticulous, step-by-step explanations for all problems found in Chapter 4 of the Class 8 NCERT Textbook, ensuring that students can grasp the intricacies of Practical Geometry.

Access Answers to NCERT Solutions for Class 8 Maths Chapter 4: Practical Geometry

Students can access the NCERT Solutions for Class 8 Maths Chapter 4: Practical Geometry. Curated by experts according to the CBSE syllabus for 2023–2024, these step-by-step solutions make Maths much easier to understand and learn for the students. These solutions can be used in practice by students to attain skills in solving problems, reinforce important learning objectives, and be well-prepared for tests.

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

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

 

Answer :

(i)

NCERT Solution For Class 8 Maths Chapter 4 Image 1The rough sketch of the quadrilateral ABCD can be drawn as follows.

(1) ∆ABC can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 2

(2) Vertex D is 6 cm away from vertex A. Therefore, while taking A as the centre, draw an arc of radius 6 cm.

NCERT Solution For Class 8 Maths Chapter 4 Image 3

(3) Taking C as the centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Joint D to A and C.

NCERT Solution For Class 8 Maths Chapter 4 Image 4

ABCD is the required quadrilateral.

(ii)

The rough sketch of the quadrilateral JUMP can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 5

(1) ∆ JUP can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 6

(2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm, respectively. Let the point of intersection be M.

NCERT Solution For Class 8 Maths Chapter 4 Image 7

(3) Join M to P and U.

NCERT Solution For Class 8 Maths Chapter 4 Image 8

JUMP is the required quadrilateral.

(iii)

We know that opposite sides of a parallelogram are equal in length, and also, these are parallel to each other.

i.e., ME = OR, MO = ER

NCERT Solution For Class 8 Maths Chapter 4 Image 9The rough sketch of the parallelogram MORE can be drawn as follows.

(1) ∆ EOR can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 10

(2) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Therefore, while taking O and E as centres, draw arcs of 4.5 cm radius and 6 cm radius, respectively. These will intersect each other at point M.

NCERT Solution For Class 8 Maths Chapter 4 Image 11

(3) Join M to O and E.

NCERT Solution For Class 8 Maths Chapter 4 Image 12

MORE is the required parallelogram.

(iv)

We know that all sides of a rhombus are of the same measure. Hence, BE = ES = ST = TB

The rough sketch of the rhombus BEST can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 13

NCERT Solution For Class 8 Maths Chapter 4 Image 14(1) ∆ BET can be constructed by using the given measurements as follows.

(2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will intersect each other at point S.

NCERT Solution For Class 8 Maths Chapter 4 Image15

(3) Join S to E and T.

NCERT Solution For Class 8 Maths Chapter 4 Image
NCERT Solution For Class 8 Maths Chapter 4 Image 16

BEST is the required rhombus.

 


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

 

 

Answer :

(i) A rough sketch of the quadrilateral LIFT can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 17

(1) ∆ ITL can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 18

(2) Vertex F is 4.5 cm away from vertex L and 3 cm away from vertex I.  ∴ while taking L and I as centres, draw arcs of 4.5 cm radius and 3 cm radius, respectively, which will intersect each other at point F.

NCERT Solution For Class 8 Maths Chapter 4 Image 19

NCERT Solution For Class 8 Maths Chapter 4 Image 20

(3) Join F to T and F to I.

LIFT is the required quadrilateral.

(ii) The rough sketch of the quadrilateral GOLD can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 21

(1) ∆ GDL can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 22

(2) Vertex O is 10 cm away from vertex D and 7.5 cm away from vertex L. Therefore, while taking D and L as centres, draw arcs of 10 cm radius and 7.5 cm radius, respectively. These will intersect each other at point O.

NCERT Solution For Class 8 Maths Chapter 4 Image 23

(3) Join O to G and L.

NCERT Solution For Class 8 Maths Chapter 4 Image 24

GOLD is the required quadrilateral.

(iii) We know that the diagonals of a rhombus always bisect each other at 90º.

Let us assume that these are intersecting each other at point O in this rhombus. Hence, EO = OD = 3.25 cm

The rough sketch of the rhombus BEND can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 25

(1) Draw a line segment BN of 5.6 cm, and also draw its perpendicular bisector. Let it intersect the line segment BN at point O.

NCERT Solution For Class 8 Maths Chapter 4 Image 26

(2) Taking O as the centre, draw arcs of 3.25 cm radius to intersect the perpendicular bisector at points D and E.

NCERT Solution For Class 8 Maths Chapter 4 Image 27

(3) Join points D and E to points B and N.

NCERT Solution For Class 8 Maths Chapter 4 Image 28

BEND is the required quadrilateral.

 


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

 

 

Answer :

(i) Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 29

NCERT Solution For Class 8 Maths Chapter 4 Image 30

(1) Draw a line segment MO of 6 cm and an angle of 105º at point O. As vertex R is 4.5 cm away from the vertex O, cut a line segment OR of 4.5 cm from this ray.

(2) Again, draw an angle of 105º at point R.

NCERT Solution For Class 8 Maths Chapter 4 Image 31

(3) Draw an angle of 60º at point M. Let this ray meet the previously drawn ray from R at point E.

NCERT Solution For Class 8 Maths Chapter 4 Image 32

MORE is the required quadrilateral.

(ii) The sum of the angles of a quadrilateral is 360°. In quadrilateral PLAN,

∠P + ∠L + ∠A + ∠N = 360° 90° + ∠L + 110° + 85° = 360°

285° + ∠L = 360°

∠L = 360° − 285° = 75°

Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 33

(1) Draw a line segment PL of 4 cm and draw an angle of 75º at point L. As vertex A is 6.5 cm away from vertex L, cut a line segment LA of 6.5 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 34

(2) Again, draw an angle of 110º at point A.

NCERT Solution For Class 8 Maths Chapter 4 Image 35

(3) Draw an angle of 90º at point P. This ray will meet the previously drawn ray from A at point N.

NCERT Solution For Class 8 Maths Chapter 4 Image 36

PLAN is the required quadrilateral.

(iii) Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 37

(1) Draw a line segment HE of 5 cm and an angle of 85º at point E. As vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 38

(2) Vertex R is 6 cm and 5 cm away from vertex H and A, respectively. By taking radii as 6 cm and 5 cm, draw arcs from points H and A, respectively. These will intersect each other at point R.

NCERT Solution For Class 8 Maths Chapter 4 Image 39

(3) Join R to H and A.

NCERT Solution For Class 8 Maths Chapter 4 Image 40

HEAR is the required quadrilateral.

(iv) Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 41

(1) Draw a line segment OK of 7 cm and an angle of 90º at point K. As vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 42

(2) Vertex Y is 5 cm and 7 cm away from vertex O and A, respectively. By taking

radii as 5 cm and 7 cm, draw arcs from points O and A, respectively. These will intersect each other at point Y.

NCERT Solution For Class 8 Maths Chapter 4 Image 43

(3) Join Y to A and O.

NCERT Solution For Class 8 Maths Chapter 4 Image 44

OKAY is the required quadrilateral.

 


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°

 

Answer :

(i) Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 45

(1) Draw a line segment DE of 4 cm and an angle of 60º at point E. As vertex A is 5 cm away from vertex E, cut a line segment EA of 5 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 46

(2) Again, draw an angle of 90º at point A. As vertex R is 4.5 cm away from vertex A, cut a line segment RA of 4.5 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 47

NCERT Solution For Class 8 Maths Chapter 4 Image 48

(3) Join D to R.

DEAR is the required quadrilateral.

(ii) Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 49

(1) Draw a line segment RU of 3 cm and an angle of 120º at point U. As vertex E is 4 cm away from vertex U, cut a line segment UE of 4 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 50

(2) Next, draw an angle of 75º at point R. As vertex T is 3.5 cm away from vertex R, cut a line segment RT of 3.5 cm from this ray.

NCERT Solution For Class 8 Maths Chapter 4 Image 51

(3) Join T to E.

NCERT Solution For Class 8 Maths Chapter 4 Image 52

TRUE is the required quadrilateral.

 


Exercise 4.5

Question 1 :

Draw the following:

1. The square READ with RE = 5.1 cm

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

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

4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm.

 

 

 

 

Answer :

1. All the sides of a square are of the same measure, and also, all the interior angles of a square are 90º measure. Therefore, the given square READ can be drawn as follows.

Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 53

(1) Draw a line segment RE of 5.1 cm and an angle of 90º at points R and E.

NCERT Solution For Class 8 Maths Chapter 4 Image 54

(2) As vertex A and D are 5.1 cm away from vertex E and R, respectively, cut line segments EA and RD, each of 5.1 cm from these rays.

NCERT Solution For Class 8 Maths Chapter 4 Image 55

(3) Join D to A.

NCERT Solution For Class 8 Maths Chapter 4 Image 56

READ is the required square.

2. In a rhombus, diagonals bisect each other at 90º. ∴, the given rhombus ABCD can be drawn as follows.

Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 57

(1) Draw a line segment AC of 5.2 cm and draw its perpendicular bisector. Let it intersect the line segment AC at point O.

NCERT Solution For Class 8 Maths Chapter 4 Image 58

(2) Draw arcs of 6.4/2 = 3.2 on both sides of this perpendicular bisector. Let the arcs intersect the perpendicular bisector at points B and D.

NCERT Solution For Class 8 Maths Chapter 4 Image 59

(3) Join points B and D with points A and C.

NCERT Solution For Class 8 Maths Chapter 4 Image 60

ABCD is the required rhombus.

3.  Opposite sides of a rectangle have lengths of the same measure, and also, all the interior angles of a rectangle are 90º measure. The given rectangle ABCD may be drawn as follows.

Rough figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 61

(1) Draw a line segment AB of 5 cm and an angle of 90º at points A and B.

NCERT Solution For Class 8 Maths Chapter 4 Image 62

(2) As vertex C and D are 4 cm away from vertex B and A, respectively, cut line segments AD and BC, each of 4 cm, from these rays.

NCERT Solution For Class 8 Maths Chapter 4 Image 63

(3) Join D to C.

NCERT Solution For Class 8 Maths Chapter 4 Image 64

ABCD is the required rectangle.

4. Opposite sides of a parallelogram are equal and parallel to each other. The given parallelogram OKAY can be drawn as follows.

Rough Figure:

NCERT Solution For Class 8 Maths Chapter 4 Image 65

(1) Draw a line segment OK of 5.5 cm and a ray at point K at a convenient angle.

NCERT Solution For Class 8 Maths Chapter 4 Image 66

(2) Draw a ray at point O parallel to the ray at K. As the vertices A and Y are 4.2 cm away from the vertices K and O, respectively, cut line segments KA and OY, each of 4.2 cm, from these rays.

NCERT Solution For Class 8 Maths Chapter 4 Image 67

(3) Join Y to A.

NCERT Solution For Class 8 Maths Chapter 4 Image 68

OKAY is the required rectangle.

 


Frequently Asked Questions

The NCERT solution for class 8 Chapter 4: Practical Geometry is important as it provides a structured approach to learning, ensuring that students develop a strong understanding of foundational concepts early in their academic journey. By mastering these basics, students can build confidence and readiness for tacking more difficult concepts in their further education.

Yes, the NCERT solution for class 8 Chapter 4: Practical Geometry is quite useful for students in preparing for their exams. The solutions are simple, clear, and concise allowing students to understand them better. Practical Geometry ally, they can solve the practice questions and exercises that allow them to get exam-ready in no time.

You can get all the NCERT solutions for class 8 Maths Chapter 4  from the official website of the Orchids International School. These solutions are tailored by subject matter experts and are very easy to understand. 

 

Yes, students must practice all the questions provided in the NCERT solution for class 8 Maths Chapter 4 : Practical Geometry  as it will help them gain a comprehensive understanding of the concept, identify their weak areas, and strengthen their preparation. 

Students can utilize the NCERT solution for class 8 Maths Chapter 4  effectively by practicing the solutions regularly. Solve the exercises and practice questions given in the solution. Also, you can make Practical Geometry al notes and jot down the important concepts for your understanding.

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