ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1
Question 1.
Construct a quadrilateral PQRS where PQ = 4.5 cm, QR = 6 cm, RS = 5.5 cm, PS = 5 cm and PR = 6.5 cm.
Solution:
Steps of constructions :
(i) Draw a line segment PR = 6.5 cm.
(ii) With centre P and radius 4.5 cm and with centre R
and radius 6 cm draw arcs intersecting each other at Q.
(iii) Join PQ and QR.
(iv) Similarly with centre P and radius 5 cm and with centre R
and radius 5.5 cm, draw arcs intersecting each other at S.
(v) Join PS and SR.
PQRS is the required quadrilateral.
Question 2.
Construct a quadrilateral ABCD in which AB = 3·5 cm, BC = 5 cm, CD = 5·6 cm, DA = 4 cm and BD = 5·4 cm
Solution:
Steps of construction :
(i) Draw AB = 3·5 cm.
(ii) With A as centre and radius = 4 cm,
draw an arc with B as centre and radius = 5·4 cm
draw an arc to meet the previous arc at D. Join AD andBD.
(iii) With B as centre and radius = 5 cm,
draw an arc With D as centre and radius = 5·6 cm,
draw an arc to meet the previous arc at C.
(iv) Join BC and CD, then ABCD is the required quadrilateral.
Question 3.
Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2·5 cm, PS = 3·5 cm, PR = 4 cm and QS = 5 cm.
Solution:
Steps of construction :
(i) Draw PQ = 3 cm.
(ii) With P as centre and radius = 4 cm,
draw an arc with Q as centre and radius = 2·5 cm
draw an arc to meet the previous arc at R.
Join PR and QR.
(iii) With P as centre and radius = 3·5 cm,
draw an arc. With Q as centre and radius = 5 cm,
draw an arc to meet the previous arc at S.
(iv) Join PS, QS and SR.
(v) Hence, PQRS is the required quadrilateral.
Question 4.
Construct a quadrilateral ABCD such that BC = 5 cm, AD = 5.5 cm, CD = 4.5 cm, AC = 7 cm, and BC = 5.5 cm.
Solution:
Steps of construction :
(i) Draw a line segment CD = 4.5 cm.
(ii) With centre C and radius of 5.5 cm and with centre D
and radius 7 cm draw arcs intersecting each other at B.
(iii) Join BC and BD.
(iv) Similarly with centre C and radius 5.5 cm
and with centre D and radius 5.5 cm,
draw arcs intersecting each other at A.
(v) Join AC and AD.
(vi) Join AB.
ABCD is the required quadrilateral.
Question 5.
Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.
Solution:
Steps of construction :
(i) Draw BC = 6 cm.
(ii) At B, construct ∠CBP = 45°.
(iii) At C, construct ∠BCQ = 90°
(iv) From CQ, cut off CD = 4 cm.
(v) At D, construct ∠CDR = 120°.
(vi) Let BP and DR meet at A.
Then ABCD is the required quadrilateral.
Question 6.
Construct a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, ∠P = 60°, ∠Q = 90° and ∠R = 120°.
Solution:
Steps of construction :
(i) Draw a line segment QR = 6 cm.
(ii) At Q, draw a ray QX making an angle of 90°
and cut off QP = 4 cm.
(iii) At P, draw a ray making an angle of 60° and at R,
a ray making an angle 120° which meet each other at S.
PQRS is the required quadrilateral.
Question 7.
Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4·2 cm, AD = 3·5 cm, ∠A = 90°, and ∠B = 60°
Solution:
Steps of construction :
(i) Draw AB = 5 cm.
(ii) At A, construct angle A = 90°
(iii) At B, construct angle B = 60°
(iv) With B as centre and 4·2 cm as radius, cut off ∠B atC.
(v) With A as centre and 3·5 cm as radius, cut off ∠A at D.
(vi) Join CD. Then ABCD is the required quadrilateral.
Question 8.
Cosntruct a quadrilateral PQRS where PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, ∠Q = 60° and ∠R = 90°.
Solution:
Steps of construction :
(i) Draw a line segment QR = 5 cm.
(ii) At Q, draw a ray QX making an angle of 60°
and cut off QP = 4 cm.
(iii) At R, draw a ray RY making an angle of 90°
and cut off RS. = 4.5 cm.
(iv) Join PS.
PQRS is the required quadrilateral.
Question 9.
Construct a quadrilateral BEST where BE = 3.8 cm, ES = 3.4 cm, ST = 4.5 cm, TB = 5 cm and ∠E = 80°.
Solution:
Steps of construction :
(i) Draw a line segment BE = 3.8 cm.
(ii) At E, draw a ray EX making an angle of 80°
and cut off ES = 3.4 cm.
(iii) With centre B and radius 5 cm and
with centre S with radius 4.5 cm,
draw arcs intersecting each other at T.
(iv) Join TB and TS.
BEST is the required quadrilateral.
Question 10.
Construct a quadrilateral ABCD where AB = 4·5 cm, BC = 4 cm, CD = 3·9 cm, AD = 3·2 cm and ∠B = 60°.
Solution:
Steps of construction :
(i) Draw AB = 4·5 cm.
(ii) At B, construct ∠ABP = 60°.
(iii) From BP, cut of ∠BC = 4 cm.
(iv) With C as centre, and 3·9 cm as radius draw an arc.
(v) With A as centre and 3·2 cm as radius,
draw an arc to meet the previous arc at D.
(vi) Join AD and CD.
