NCERT Class 8 Mathematics Solutions: Chapter 4 – Practical Geometry Exercise 4.1 Part 1

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To construct various quadrilaterals through given values

Construction of Quadrilaterals

To construct various quadrilaterals through given values

Question: 1 Construct the following quadrilaterals:

(i) Quadrilateral ABCD

(ii) Quadrilateral JUMP

(iii) Parallelogram MORE

(iv) Rhombus BEST

Answer:

(i)

Given,

To construction a quadrilateral ABCD

Step of construction:-

(1) Draw

(2) Draw in arc. Taking radius 5.5 cm from point B.

(3) Taking radius 7 cm, draw another arc from point A. which intersects the first arc at point C,

(4) Join AC and BC.

(5) Draw an arc of radius 6 cm from point A and draw another arc of radius 4 cm from point C which intersects at D, making in .

(6) Join AD and DC.

It is quadrilateral ABCD.

Image

A Quadrilateral ABCD

Construction of quadrilateral ABCD

(ii)

Given,

To construction a quadrilateral JUMP

Step of construction:-

(1) Draw

(2) Draw an arc of radius 4.5 cm taking centre J and then draw another arc of radius 6.5cm taking U as centre. Both arcs intersect at P.

(3) Join PJ and PU.

(4) Draw arc of radius 5 cm and 4 cm taking P and U as centres respectively, which intersect at M.

(5)Join MP and MU.

It is quadrilateral JUMP.

Image

A Quadrilateral JUMP

construction of quadrilateral JUMP

(iii)

Given,

To construction, Parallelogram MORE.

Step of construction:-

(1) Draw

(2) Draw arcs of radius 7.5 cm and radius 4.5 cm taking O and R as centres respectively, which intersect at E.

(3) Join OE and RE.

(4) Draw an arc of 6 cm radius taking E as centre.

(5) Draw another arc of 4.5 cm radius taking O as centre, which intersects at M.

(6) Join OM and EM.

It is parallelogram MORE.

Image

Figure of Parallelogram MORE

Contraction of parallelogram MORE

(iv)

Given,

To construction a rhombus BEST.

Step of construction:-

(1) Draw and bisect it into two equal parts.

(2) Draw up and down perpendiculars to TE.

(3) Draw two arcs of 4.5 cm taking E and T as centres, which intersect at S.

(4) Again draw two arcs of 4.5 cm taking E and T as centres, which intersect at B.

(5) Join TS, ES, BT and EB

It is a rhombus BEST.

Image

A Figure is Rhombus BEST

Construction of rhombus BEST