**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.1**

Ex 4.1 Class 8 Maths 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) We have to draw first rough sketch.

Construction:

StepI: Draw AB = 4.5 cm

Step II: Draw an arc with centre B and radius 5.5 cm.

StepIII: Draw another arc with centre A and radius 7 cm to meet the previous arc at C.

Step IV: Draw an arc with centre C and radius 4 cm.

StepV: Draw another arc with centre A and radius 6 cm to cut the former arc at D.

Step VI: Join BC, AC, CD and AD.

(ii) We have to draw the first rough sketch.

Thus ABCD is the required quadrilateral.

Construction:

StepI: Draw JU = 3.5 cm.

Step II: Draw an arc with centre J and radius 4.5 cm.

StepIII: Draw another arc with centre U and radius 6.5 cm to meet the previous arc at P.

Step IV: Join JP and UP.

StepV: Draw an arc with centre U and radius 4 cm.

Step VI: Draw another arc with centre P and radius 5 cm to meet the previous arc at M.

StepVII: Join UM and PM.

Thus, JUMP is the required quadrilateral.

(iii) We have to draw the first rough sketch.

Construction: (Opposite sides of a parallelogram are equal)

StepI: Draw OR = 6 cm.

Step II: Draw an arc with centre R and radius 4.5 cm.

StepIII: Draw another arc with centre O and radius 7.5 cm to meet the previous arc at E.

Step IV: Join RE and OE.

StepV: Draw an arc with centre E and radius 6 cm.

Step VI: Draw another arc with centre O and radius 4.5 cm to meet the former arc at M.

StepVII: Join EM and OM.

Thus, MORE is the required parallelogram.

(iv) We have to draw first rough sketch.

Construction: (All sides of a rhombus are equal)

Step I: Draw BE = 4.5 cm

StepII: Draw an arc with centre B and radius 4.5 cm.

Step III: Draw another arc with centre E and radius 6 cm to meet the previous arc at T.

StepIV: Join BT and ET.

Step V: Draw two arcs with centres E and T with equal radii 4-5 cm to meet each other at S. .

StepVI: Join ES and TS.

Thus, BEST is the required rhombus.

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