## Book: NCERT - Mathematics

### Chapter: 4. Practical Geometry

#### Subject: Maths - Class 8th

##### Q. No. 1 of Exercises 4.2

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##### Construct the following quadrilaterals.(i) Quadrilateral LIFTLI = 4 cmIF = 3 cmTL = 2.5 cmLF = 4.5 cmIT = 4 cm(ii) Quadrilateral GOLDOL = 7.5 cmGL = 6 cmGD = 6 cmLD = 5 cmOD = 10 cm(iii) Rhombus BENDBN = 5.6 cmDE = 6.5 cm

(i) A rough sketch of this quadrilateral:

(a) Δ ITL can be constructed as follows:

(b) Vertex F is 4.5 cm away from vertex L and 3 cm away from vertex I.

Hence, taking L and I as centers, draw arcs of 4.5 cm radius and 3 cm radius respectively, which will intersect each other at point F

(c) Join F to T and F to I

(ii) A rough sketch of this quadrilateral:

(a) Δ GDL can be constructed as follows:

(b) Vertex O is 10 cm away from vertex D and 7.5 cm away from vertex L.

Hence, taking D and L as centers, draw arcs of 10 cm radius and 7.5 cm radius respectively These will intersect each other at point O

(c) Join O to G and L

(iii) We know that the diagonals of a rhombus always bisect each other at 90°

So in this case let us assume these are intersecting each other at point O

Therefore,

EO = OD = 3.25 cm

A rough sketch of this rhombus:

(a) Draw a line segment BN of 5.6 cm and its perpendicular bisector. Let it will be intersecting the line segment BN at point O

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

(c) Join points D and E to points B and N

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