NCERT Solutions for class 8 Maths chapter 4 Practical geometry exercise 4.2

Exercise 4.2

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Q 1 - Ex 4.2 - Practical Geometry - NCERT Maths Class 8th - Chapter 4

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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
Sol :
A rough sketch of this quadrilateral can be drawn as follows.

(Step-1) Δ ITL can be constructed by using the given measurements as follows.

(Step-2) Vertex F is 4.5 cm away from vertex L and 3 cm away from vertex I. Therefore, while taking L and I as centres, draw arcs of 4.5 cm radius and 3 cm radius respectively, which will be intersecting each other at point F.

(Step-3) Join F to T and F to I.

LIFT is the required quadrilateral.

(ii) Quadrilateral GOLD
OL = 7.5 cm
GL = 6 cm
GD = 6 cm
LD = 5 cm
OD = 10 cm
Sol :
A rough sketch of this quadrilateral can be drawn as follows.

(Step-1) Δ GDL can be constructed by using the given measurements as follows.

(Step-2) Vertex O is 10 cm away from vertex D and 7.5 cm away from vertex L. Therefore, while taking D and L as centres, draw arcs of 10 cm radius and 7.5 cm radius respectively. These will intersect each other at point O.

(Step-3) Join O to G and L.

GOLD is the required quadrilateral.

(iii) Rhombus BEND
BN = 5.6 cm
DE = 6.5 cm
Sol :
We know that the diagonals of a rhombus always bisect each other at 90º. Let us assume that these are intersecting each other at point O in this rhombus.
Hence, EO = OD = 3.25 cm
A rough sketch of this rhombus can be drawn as follows.

(Step-1) Draw a line segment BN of 5.6 cm and also draw its perpendicular bisector. Let it intersect the line segment BN at point O.

(Step-2) Taking O as centre, draw arcs of 3.25 cm radius to intersect the perpendicular bisector at point D and E.

(Step-3) Join points D and E to points B and N.

BEND is the required quadrilateral.