Mathematics – Class 8 – Chapter 4 – Practical Geometry – Exercise 4.1 – NCERT Exercise Solution

Construct the following quadrilaterals.

(i) Quadrilateral ABCD

AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm, AC = 7 cm

Solution:

Constructions steps:

Step I: Draw a line segment AB = 4.5 cm

Step II: With centre B draw an arc of radius 5.5 cm.

Step III: Draw another arc with centre A of radius 7 cm to meet the previous arc at C.

Step IV: With centre C draw arc of radius 4 cm.

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

Step VI: Now, join BC, AC, CD and AD.

Hence, ABCD is the required quadrilateral.

Mathematics - Class 8 - Chapter 4 - Practical Geometry - Exercise 4.1 - NCERT Exercise Solution

(ii) Quadrilateral JUMP

JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm

Solution:

Constructions steps:

Step I: Draw a line segment JU = 3.5 cm.

Step II: With centre J draw an arc of radius 4.5 cm.

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

Step IV: Join JP and UP.

Step V: With centre U draw an arc of radius 4 cm.

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

Step VII: Join UM and PM.

Hence, JUMP is the required quadrilateral.

Mathematics - Class 8 - Chapter 4 - Practical Geometry - Exercise 4.1 - NCERT Exercise Solution

(iii) Parallelogram MORE

OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm

Solution:

Constructions steps:

(We know that opposite sides of a parallelogram are equal)

Step I: Draw a line segment OR = 6 cm.

Step II: With centre R draw an arc of radius 4.5 cm.

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

Step IV: Join RE and OE.

Step V: With centre E draw an arc of radius 6 cm.

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

Step VII: Join EM and OM.

Hence, MORE is the required parallelogram.

Mathematics - Class 8 - Chapter 4 - Practical Geometry - Exercise 4.1 - NCERT Exercise Solution

(iv) Rhombus BEST

BE = 4.5 cm, ET = 6 cm

Solution:

Constructions steps:

(We know that all sides of a rhombus are equal)

Step I: Draw BE = 4.5 cm

Step II: With centre B draw an arc of radius 4.5 cm.

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

Step IV: 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.

Step VI: Join ES and TS.

Hence, BEST is the required rhombus.

Mathematics - Class 8 - Chapter 4 - Practical Geometry - Exercise 4.1 - NCERT Exercise Solution

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