# Practical Geometry Chapter 4 Class 8 Maths NCERT Textbook With Solutions PDF

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## NCERT Class 8 Maths Textbook Chapter 4 With Answer Book PDF Free Download

### Chapter 4:Practical Geometry

#### 4.1 Introduction

You have learned how to draw triangles in Class VII. We require three measurements (of sides and angles) to draw a unique triangle.

Since three measurements were enough to draw a triangle, a natural question arises whether four measurements would be sufficient to draw a unique four-sided closed figure, namely, a quadrilateral.

#### 4.2 Constructing a Quadrilateral

We shall learn how to construct a unique quadrilateral given the following measurements:
• When four sides and one diagonal are given.
• When two diagonals and three sides are given.
• When two adjacent sides and three angles are given.
• When three sides and two included angles are given.
• When other special properties are known.

#### 4.2.2 When two diagonals and three sides are given

When four sides and a diagonal were given, we first drew a triangle with the available data and then tried to locate the fourth point. The same technique is used here.

#### 4.2.4 When three sides and two included angles are given

Under this type, when you draw a rough sketch, note carefully the “included” angles in particular.

### NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry

(i) Quadrilateral ABCD AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm AD = 6 cm AC = 7 cm

Solution: The rough sketch of the quadrilateral ABCD can be drawn as follows.

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

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

(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.

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.

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

(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.

(3) Join M to P and U.

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 The rough sketch of the parallelogram MORE can be drawn as follows.

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

(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.

(3) Join M to O and E.

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. (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.

(3) Join S to E and T.

NCERT Solution For Class 8 Maths Chapter 4 Image BEST is the required rhombus.

NCERT Class 8 Maths Textbook Chapter 4 With Answer Book PDF Free Download