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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.

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.

 


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