Class 8 - Mathematics
Practical Geometry- Exercise 4.1
Top Block 1
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
Answer :
(i) Given: AB = 4.5 cm, BC = 5.5 cm,
CD = 4 cm, AD = 6 cm, AC = 7 cm
To construct: A quadrilateral ABCD
Steps of construction:
(a) Draw AB = 4.5 cm.
(b) Draw an arc taking radius 5.5 cm from point B.
(c) Taking radius 7 cm, draw an another arc from point A which intersects the first arc at point C.
(d) Join BC and AC.
(e) 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.
(f) Join AD and CD.
It is required quadrilateral ABCD.
(ii) Given: JU = 3.5 cm, UM = 4 cm,
MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm
To construct: A quadrilateral JUMP
Steps of construction:
(b) Draw an arc taking radius 5.5 cm from point B.
(c) Taking radius 7 cm, draw an another arc from point A which intersects the first arc at point C.
(d) Join BC and AC.
(e) 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.
(f) Join AD and CD.
It is required quadrilateral ABCD.
(ii) Given: JU = 3.5 cm, UM = 4 cm,
MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm
To construct: A quadrilateral JUMP
Steps of construction:
Mddle block 1
(a) Draw JU = 3.5 cm.
(b) Draw an arc of radius 4.5 cm taking centre J and then draw another arc of radius 6.5 cm taking U as centre. Both arcs intersect at P.
(c) Join PJ and PU.
(d) Draw arc of radius 5 cm and 4 cm taking P and U as centres respectively, which intersect at M.
(e) Join Mp and MU.
It is required quadrilateral JUMP.
(iii) Given: OR = 6 cm, RE = 4.5 cm,
EO = 7.5 cm
To construct: A parallelogram MORE.
Steps of construction:
(b) Draw an arc of radius 4.5 cm taking centre J and then draw another arc of radius 6.5 cm taking U as centre. Both arcs intersect at P.
(c) Join PJ and PU.
(d) Draw arc of radius 5 cm and 4 cm taking P and U as centres respectively, which intersect at M.
(e) Join Mp and MU.
It is required quadrilateral JUMP.
(iii) Given: OR = 6 cm, RE = 4.5 cm,
EO = 7.5 cm
To construct: A parallelogram MORE.
Steps of construction:
(a) Draw OR = 6 cm.
(b) Draw arcs of radius 7.5 cm and radius 4.5 cm taking O and R as centres respectively, which intersect at E.
(c) Join OE and RE.
(d) Draw an arc of 6 cm radius taking E as centre.
(e) Draw another arc of 4.5 cm radius taking O as centre, which intersects at M.
(f) Join OM and EM.
It is required parallelogram MORE.
(iv) Given: BE = 4.5 cm, ET = 6 cm
To construct: A rhombus BEST.
Steps of construction:
(b) Draw arcs of radius 7.5 cm and radius 4.5 cm taking O and R as centres respectively, which intersect at E.
(c) Join OE and RE.
(d) Draw an arc of 6 cm radius taking E as centre.
(e) Draw another arc of 4.5 cm radius taking O as centre, which intersects at M.
(f) Join OM and EM.
It is required parallelogram MORE.
(iv) Given: BE = 4.5 cm, ET = 6 cm
To construct: A rhombus BEST.
Steps of construction:
(a) Draw TE = 6 cm and bisect it into two equal parts.
(b) Draw up and down perpendiculars to TE.
(c) Draw two arcs of 4.5 cm taking E and T as centres, which intersect at S.
(d) Again draw two arcs of 4.5 cm taking E and T as centres, which intersects at B.
(e) Join TS, ES, BT and EB.
It is the required rhombus BEST.
(b) Draw up and down perpendiculars to TE.
(c) Draw two arcs of 4.5 cm taking E and T as centres, which intersect at S.
(d) Again draw two arcs of 4.5 cm taking E and T as centres, which intersects at B.
(e) Join TS, ES, BT and EB.
It is the required rhombus BEST.