Exercise 4.1
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 1:
(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 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:
(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:
(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:
(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.
Exercise 4.2
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
(ii) Quadrilateral GOLD
OL = 7.5 cm, GL = 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm
(iii) Rhombus BEND
BN = 5.6 cm, DE = 6.5 cm
Answer 1:
(i) Given: LI = 4 cm, IF = 3 cm, TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm
To construct: A quadrilateral LIFT
Steps of construction:
(a) Draw a line segment LI = 4 cm.
(b) Taking radius 4.5 cm, draw an arc taking L as centre.
(c) Draw an arc of 3 cm taking I as centre which intersects the first arc at F.
(d) Join FI and FL.
(e) Draw another arc of radius 2.5 cm taking L as centre and 4 cm taking I as centre which intersect at T.
(f) Join TF, Tl and TI.
It is the required quadrilateral LIFT.
(ii) Given:
OL = 7.5 cm, GL = 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm
To construct: A quadrilateral GOLD
Steps of construction:
(a) Draw a line segment OL = 7.5 cm
(b) Draw an arc of radius 5 cm taking L as centre and another arc of radius 10 cm taking O as centre which intersect the first arc point at D.
(c) Join LD and OD.
(d) Draw an arc of radius 6 cm from D and draw another arc of radius 6 cm taking L as centre, which intersects at G.
(e) Join GD and GO.
It is the required quadrilateral GOLD.
(iii) Given: BN = 5.6 cm, DE = 6.5 cm
To construct: A rhombus BEND.
Steps of construction:
(a) Draw DE = 6.5 cm.
(b) Draw perpendicular bisector of line segment DE.
(c) Draw two arcs of radius 2.8 cm from intersection point O, which intersects the line KN at B and N. (d)Join BE, BD as well as ND and NE.
It is the required rhombus BEND.
Exercise 4.3
Question 1:
Construct the following quadrilaterals:
[i] Quadrilateral MORE
MO = 6 cm, OR = 4.5 cm, ∠M = 60% ∠O = 105^{o} , ∠R = 105°
[ii] Quadrilateral PLAN
PL = 4 cm, LA = 6.5 cm, ∠P = 90^{o} ∠A = 110^{o} ∠N = 85^{0}
(iii) Parallelogram HEAR
HE = 5 cm, EA = 6 cm, ∠R = 85^{0}
Rectangle OKAY
OK = 7 cm, KA = 5 cm
Answer 1:
(i) Given: MO = 6 cm, OR = 4.5 cm, M = 60^{o} , O = 105^{o} , R = 105^{o}
To construct: A quadrilateral MORE.
Steps of construction:
(a) Draw a line segment MO = 6 cm.
(b) Construct R = 105^{o} and taking radius 4.5 cm, draw an arc taking O as centre, which intersects at R.
(c) Also construct an angle 105^{o} at R and produce the side RE.
(d) Construct another angle of 60^{o} at point M and produce the side ME. Both sides ME and RE intersect at E.
It is the required quadrilateral MORE.
(ii) Given: PL = 4 cm, LA = 6.5 cm, P = 90^{o} , A = 110^{o} , N = 85^{o}
To construct: A quadrilateral PLAN.
To find: ∠L = 360^{0}  (90 + 85^{0 }+ 110°) = 360^{o } 285^{o }= 75^{o}
Steps of construction:
It is the required quadrilateral PLAN.
(iii) Given: HE = 5 cm, EA = 6 cm, R = 85^{o}
To construct: A parallelogram HEAR.
To find: ∠H = 180°  85^{o} = 95° [ ∵Sum of adjacent angle of ^{g}^{m} is 180^{0}]
Steps of construction:
It is the required parallelogram HEAR.
(iv) Given: OK = 7 cm, KA = 5 cm
To construct: A rectangle OKAY.
Steps of construction:
It is the required rectangle OKAY.
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