Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only)

Constructions Exercise 18A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Given below are the angles x and y.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A Q1
Without measuring these angles, construct :
(i) ∠ABC = x + y
(ii) ∠ABC = 2x + y
(iii) ∠ABC = x + 2y
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 3

Question 2.
Given below are the angles x, y and z.
Without measuring these angles construct :
(i) ∠ABC = x + y + z
(ii) ∠ABC = 2x + y + z
(iii) ∠ABC = x + 2y + z
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 4
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 5
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 6

Question 3.
Draw a line segment BC = 4 cm. Construct angle ABC = 60°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 7

Question 4.
Construct angle ABC = 45° in which BC = 5 cm and AB = 4.6 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 8

Question 5.
Construct angle ABC = 90°. Draw BP, the bisector of angle ABC. State the measure of angle PBC.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 9

Question 6.
6. Draw angle ABC of any suitable measure.
(i) Draw BP, the bisector of angle ABC.
(ii) Draw BR, the bisector of angle PBC and draw BQ, the bisector of angle ABP.
(iii) Are the angles ABQ, QBP, PBR and RBC equal?
(iv) Are the angles ABR and QBC equal ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18A 10

Constructions Exercise 18B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Draw a line segment AB of length 5.3 cm. Using two different methods bisect AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 11
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 12

Question 2.
Draw a line segment PQ = 4.8 cm. Construct the perpendicular bisector of PQ.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 13

Question 3.
In each of the following, draw perpendicular through point P to the line segment AB :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 14
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 15
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 16

Question 4.
Draw a line segment AB = 5.5 cm. Mark a point P, such that PA = 6 cm and PB = 4.8 cm. From the point P, draw a perpendicular to AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 17

Question 5.
Draw a line segment AB = 6.2 cm. Mark a point P in AB such that BP = 4 cm. Through point P draw perpendicular to AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18B 18

Constructions Exercise 18C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Draw a line AB = 6 cm. Mark a point P any where outside the line AB. Through the point P, construct a line parallel to AB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 19

Question 2.
Draw a line MN = 5.8 cm. Locate a point A which is 4.5 cm from M and 5 cm from N. Through A draw a line parallel to line MN.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 20

Question 3.
Draw a straight line AB = 6.5 cm. Draw another line which is parallel to AB at a distance of 2.8 cm from it.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 21

Question 4.
Construct an angle PQR = 80°. Draw a line parallel to PQ at a distance of 3 cm from it and another line parallel to QR at a distance of 3.5 cm from it. Mark the point of intersection of these parallel lines as A.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 22

Question 5.
Draw an angle ABC = 60°. Draw the bisector of it. Also draw a line parallel to BC a distance of 2.5 cm from it.
Let this parallel line meet AB at point P and angle bisector at point Q. Measure the length of BP and PQ. Is BP = PQ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 23

Question 6.
Construct an angle ABC = 90°. Locate a point P which is 2.5 cm from AB and 3.2 cm from BC.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18C 24

Constructions Exercise 18D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Construct a quadrilateral ABCD; if:
(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and angle ABC = 75°.
(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and ∠BCD = 60°.
(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, ∠A = 60° and ∠B = 75°.
(iv) AB = 5 cm, BC = 6.5 cm, CD =4.8 cm, ∠B = 75° and ∠C = 120°.
(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.
(vi) AB = AD = 5cm, BD = 7 cm and BC = DC = 5.5 cm
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 25
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 26
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 27
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 28
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 29
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 30
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 31
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 32

Question 2.
Construct a parallelogram ABCD, if :
(i) AB = 3.6 cm, BC = 4.5 cm and ∠ABC = 120°.
(ii) BC = 4.5 cm, CD = 5.2 cm and ∠ADC = 75°.
(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.
(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.
(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75°.
(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is 45°.
(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between them is 60°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 33
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 34
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 35
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 36
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 37
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 38
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 39
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 40
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 41

Question 3.
Construct a rectangle ABCD ; if :
(i) AB = 4.5 cm and BC = 5.5 cm.
(ii) BC = 61 cm and CD = 6.8 cm.
(iii) AB = 5.0 cm and diagonal AC = 6.7 cm.
(iv) AD = 4.8 cm and diagonal AC = 6.4 cm.
(v) each diagonal is 6 cm and the angle between them is 45°.
(vi) each diagonal is 5.5 cm and the angle between them is 60°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 42
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 43
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 44
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 45
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 46
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 47

Question 4.
Construct a rhombus ABCD, if ;
(i) AB = 4 cm and ∠B = 120°.
(ii) BC = 4.7 cm and ∠B = 75°.
(iii) CD = 5 cm and diagonal BD = 8.5 cm.
(iv) BC = 4.8cm, and diagonal AC = 7cm.
(v) diagonal AC = 6 cm and diagonal BD = 5.8 cm.
(vi) diagonal AC = 4.9 cm and diagonal BD = 6 cm.
(vii) diagonal AC = 6.6 cm and diagonal BD = 5.3 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 48
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 49
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 50
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 51
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 52
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 53
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 54

Question 5.
Construct a square, if :
(i) its one side is 3.8 cm.
(ii) its each side is 4.3 cm.
(iii) one diagonal is 6.2 cm.
(iv) each diagonal is 5.7 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 55
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 56
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 57
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 58

Question 6.
Construct a quadrilateral ABCD in which ; ∠A = 120°, ∠B = 60°, AB = 4 cm, BC = 4.5 cm and CD = 5 cm.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 59
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 60

Question 7.
Construct a quadrilateral ABCD, such that AB = BC = CD = 4.4 cm, ∠B = 90° and ∠C = 120°.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 61
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 62

Question 8.
Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and ∠DAB = 60°. In the same figure draw the bisector of angle DAB and let it meet DC at point P. Measure angle APB.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 63

Question 9.
Draw a parallelogram ABCD, with AB = 6 cm, AD = 4.8 cm and ∠DAB = 45°. Draw the perpendicular bisector of side AD and let it meet AD at point P. Also draw the diagonals AC and BD ; and let they intersect at point O. Join O and P. Measure OP.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 64

Question 10.
Using ruler and compasses only, construct a rhombus whose diagonals are 8 cm and 6 cm. Measure the length of its one side.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 18 Constructions (Using ruler and compass only) Ex 18D 65

Selina Concise Mathematics Class 8 ICSE Solutions