## MP Board Class 8th Maths Solutions Chapter 4 Practical Geometry Ex 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

Solution:

(i) Steps of Construction:

Step-1: Draw LI = 4 cm.

Step-2: With L as centre and radius equal to 2.5 cm, cut an arc.

Step-3: With I as centre and radius equal to 4 cm, cut another arc on the arc drawn in step-2 at point T.

Step-4 : With I as centre and radius equal to 3 cm, cut an arc.

Step-5: With L as centre and radius equal to 4.5 cm, cut another arc on the arc drawn in step-4 at point F.

Step-6 : Join LT, IT, LF, IF and TF.

Hence, LIFT is the required quadrilateral.

(ii) Steps of Construction:

Step-1: Draw OL = 7.5 cm.

Step-2: With L as centre and radius equal to 5 cm cut an arc.

Step-3 : With O as centre and radius equal to 10 cm, cut another arc on the arc drawn in step-2 at point D.

Step-4: With L as centre and radius equal to 6 cm, cut another arc.

Step-5: With D as centre and radius equal to 6 cm cut an arc on arc drawn in step-4 at point G.

Step-6 : Join LD, LG, OG, OD and DG. Hence, GOLD is the required quadrilateral.

(iii) Here, BN = 5.6 cm and DE = 6.5 cm are given. These two sides are diagonals of a rhombus BEND. We know that diagonals of a rhombus bisect each other at right angles.

Steps of Construction:

Step-1: Draw BN = 5.6 cm.

Step-2 : Draw perpendicular bisector XY of BN which intersect BN at O.

Step-3 : Cut off OD = OF = 3.25 cm on \(\overrightarrow{\mathrm{OX}}\) and \(\overrightarrow{\mathrm{OY}}\) respectively.

Step-4 : Join BD, ND, BE and NE.

Hence, BEND is the required rhombus.