These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 4 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 cm

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Solution:

(i)

Steps of Construction:

I. Draw a line segment AB = 4.5 cm.

II. With centre at A and radius = 7 cm, draw an arc.

III. With centre at B and radius = 5.5 cm, draw another arc to intersect the previous arc at C.

IV. With centre at A and radius = 6 cm, draw an arc on the side opposite to that of B.

V. With centre at C and radius = 4 cm, draw another arc to intersect the previous arc at D.

VI. Join AC, BC, DA, and DC. Thus, ABCD is the required quadrilateral.

(ii)

Steps of Construction:

I. Draw a line segment JU = 3.5 cm.

II. With centre at U and radius UP = 6.5 cm, draw an arc.

III. With centre at J and radius = 4.5 cm, draw another arc to intersect the previous arc at P.

IV. With centre at U and radius = 4 cm, draw an arc on the side opposite to that of J.

V. With centre at P and radius = 4 cm, draw another arc intersecting the previous arc at M.

VI. Join PJ, PU, PM, and UM. Thus, JUMP is the required quadrilateral.

(iii)

Note: In a parallelogram opposite sides are equal.

Steps of Construction:

I. Draw a line segment MO = 4.5 cm

II. With centre O and radius = 7.5 cm, draw an arc.

III. With centre M and radius = 6 cm, draw another arc to intersect the previous arc at E.

IV. With centre at O and radius = 6 cm, draw an arc on the side opposite to E

V. With centre at E and radius = 4.5 cm, draw another arc to intersect the previous arc at R.

VI. Join OR, RE, EO, and EM. Thus, MORE is the required parallelogram.

(iv)

Steps of constructions:

I. Draw a line segment BE = 4.5 cm.

II. With centre at E and radius = 6 cm, draw an arc.

III. With centre at B and radius = 4.5 cm, draw another arc to intersect the previous arc at T.

Note: All 4 sides of a rhombus are equal.

IV. Join TB and TE.

V. With centre at T and radius = 4.5 cm, draw an arc on the side opposite to that of B.

VI. With centre at E and radius = 4.5 cm, draw another arc to intersect the previous arc at S.

VII. Join ST and SE. Thus, BEST is the required rhombus.