NCERT Solutions For Class 8 Maths Chapter 4 Practical Geometry

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry are useful for students as it helps them in scoring high marks in the examination. These NCERT Solutions contain detailed step-by-step explanations of all the problems that come under the Chapter 4 Practical Geometry of the Class 8 NCERT Textbook. By understanding the concepts used in NCERT Solutions for Class 8, students will be able to clear all their doubts related to Practical Geometry. These solutions are prepared by subject matter experts at BYJU’S, describing the complete method of solving problems.

Download PDF of NCERT Solutions for Class 8 Maths Chapter 4- Practical Geometry

 

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Access Answers of Maths NCERT Class 8 Chapter 4 – Practical Geometry

Exercise 4.1 Page: 60

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

Solution:

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 centre, draw an arc of radius 6 cm.

NCERT Solution For Class 8 Maths Chapter 4 Image 3

(3) Taking C as 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) Quadrilateral JUMP JU = 3.5 cm

UM = 4 cm MP = 5 cm PJ = 4.5 cm PU = 6.5 cm

Solution:

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) Parallelogram MORE

OR = 6 cm

Solution:

RE = 4.5 cm

EO = 7.5

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) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Solution:

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 be intersecting 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 Page: 62

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

Solution:

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 be intersecting 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) Quadrilateral GOLD OL = 7.5 cm

GL = 6 cm GD = 6 cm LD = 5 cm OD = 10 cm

Solution:

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) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

Solution:

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 centre, draw arcs of 3.25 cm radius to intersect the perpendicular bisector at point 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 Page: 64

1. Construct the following quadrilaterals.

(i) Quadrilateral MORE MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

Solution:

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) Quadrilateral PLAN PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

Solution:

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) Parallelogram HEAR HE = 5 cm

EA = 6 cm

∠R = 85°

Solution:

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 radius as 6 cm and 5 cm, draw arcs from point H and A respectively. These will be intersecting 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) Rectangle OKAY

OK = 7 cm KA = 5 cm

Solution:

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

radius as 5 cm and 7 cm, draw arcs from point O and A respectively. These will be intersecting 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 Page: 67

1. Construct the following quadrilaterals,

(i) Quadrilateral DEAR DE = 4 cm

EA = 5 cm AR

= 4.5 cm

∠E = 60°

∠A = 90°

Solution:

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) Quadrilateral TRUE TR = 3.5 cm

RU = 3 cm UE = 4 cm

∠R = 75°

∠U = 120°

Solution:

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 Page: 68

Draw the following:

1. The square READ with RE = 5.1 cm

Solution:

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

NCERT Solution For Class 8 Maths Chapter 4 Image 53Rough Figure:

(1) Draw a line segment RE of 5.1 cm and an angle of 90º at point 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. A rhombus whose diagonals are 5.2 cm and 6.4 cm long. Solution:

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

NCERT Solution For Class 8 Maths Chapter 4 Image 57Rough Figure:

(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 point 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. A rectangle with adjacent sides of length 5 cm and 4 cm. Solution:

Opposite sides of a rectangle have their lengths of same measure and also, all the interior angles of a rectangle are of 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 point 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. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Solution:

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.


NCERT Solutions for Class 8 Maths Chapter 4- Practical Geometry

The major concepts covered in the Chapter 4- Practical Geometry of include: 4.1 Introduction 4.2 Constructing a Quadrilateral 4.2.1 When the lengths of four sides and a diagonal are given 4.2.2 When two diagonals and three sides are given 4.2.3 When two adjacent sides and three angles are known 4.2.4 When three sides and two included angles are given 4.3 Some special cases
Exercise 4.1 Solutions 1 Question
Exercise 4.2 Solutions 1 Question
Exercise 4.3 Solutions 1 Question
Exercise 4.4 Solutions 1 Question
Exercise 4.5 Solutions 4 Questions

The Chapter 4 of NCERT Solutions for Class 8 Maths discusses the following:

  1. Five measurements can determine a quadrilateral uniquely.
  2. A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.
  3. A quadrilateral can be constructed uniquely if its two diagonals and three sides are known.
  4. A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are known.
  5. A quadrilateral can be constructed uniquely if its three sides and two included angles are given.

Learning the chapter Practical Geometry enables the students to:

  • Construction of Quadrilaterals:
    • Given four sides and one diagonal
    • Three sides and two diagonals
    • Three sides and two included angles
    • Two adjacent sides and three angles

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