Selina Textbook Solutions: Constructions | Mathematics Class 8 ICSE PDF Download

 Page 1


18. Constructions 
(Using ruler and compass only) 
EXERCISE 18(A) 
Question 1. 
Given below are the angles x and y. 
 
Without measuring these angles, construct : 
(i) ?ABC = x + y 
(ii) ?ABC = 2x + y 
(iii) ?ABC = x + 2y 
Solution: 
 
(i) Steps of Construction : 
1. Draw a line segment BC of any suitable length. 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
arc x at points P and Q and arms of angle y at points R and S. 
3. From the arc, with centre B, cut DE = PQ arc of x and EF = RS arc of y 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y 
Page 2


18. Constructions 
(Using ruler and compass only) 
EXERCISE 18(A) 
Question 1. 
Given below are the angles x and y. 
 
Without measuring these angles, construct : 
(i) ?ABC = x + y 
(ii) ?ABC = 2x + y 
(iii) ?ABC = x + 2y 
Solution: 
 
(i) Steps of Construction : 
1. Draw a line segment BC of any suitable length. 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
arc x at points P and Q and arms of angle y at points R and S. 
3. From the arc, with centre B, cut DE = PQ arc of x and EF = RS arc of y 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y 
(ii) Steps of Construction : 
 
Proceed in exactly the same way as in part(i) 
takes DE = PQ = arc of x. 
EF = PQ = arc of x and FG = RS = arc of y. 
Join BG and produce it upto A. 
Thus ?ABC = x + x+ y = 2x + y 
(iii) Steps of Construction : 
 
Proceed in exactly the same way as in (ii) 
taking DE = PQ = arc of x. and EF = RS = arc of y and FG = RS = arc of y. 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y + y = x + 2y 
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 
Page 3


18. Constructions 
(Using ruler and compass only) 
EXERCISE 18(A) 
Question 1. 
Given below are the angles x and y. 
 
Without measuring these angles, construct : 
(i) ?ABC = x + y 
(ii) ?ABC = 2x + y 
(iii) ?ABC = x + 2y 
Solution: 
 
(i) Steps of Construction : 
1. Draw a line segment BC of any suitable length. 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
arc x at points P and Q and arms of angle y at points R and S. 
3. From the arc, with centre B, cut DE = PQ arc of x and EF = RS arc of y 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y 
(ii) Steps of Construction : 
 
Proceed in exactly the same way as in part(i) 
takes DE = PQ = arc of x. 
EF = PQ = arc of x and FG = RS = arc of y. 
Join BG and produce it upto A. 
Thus ?ABC = x + x+ y = 2x + y 
(iii) Steps of Construction : 
 
Proceed in exactly the same way as in (ii) 
taking DE = PQ = arc of x. and EF = RS = arc of y and FG = RS = arc of y. 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y + y = x + 2y 
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 
 
Solution: 
(i) Steps of Construction : 
 
Page 4


18. Constructions 
(Using ruler and compass only) 
EXERCISE 18(A) 
Question 1. 
Given below are the angles x and y. 
 
Without measuring these angles, construct : 
(i) ?ABC = x + y 
(ii) ?ABC = 2x + y 
(iii) ?ABC = x + 2y 
Solution: 
 
(i) Steps of Construction : 
1. Draw a line segment BC of any suitable length. 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
arc x at points P and Q and arms of angle y at points R and S. 
3. From the arc, with centre B, cut DE = PQ arc of x and EF = RS arc of y 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y 
(ii) Steps of Construction : 
 
Proceed in exactly the same way as in part(i) 
takes DE = PQ = arc of x. 
EF = PQ = arc of x and FG = RS = arc of y. 
Join BG and produce it upto A. 
Thus ?ABC = x + x+ y = 2x + y 
(iii) Steps of Construction : 
 
Proceed in exactly the same way as in (ii) 
taking DE = PQ = arc of x. and EF = RS = arc of y and FG = RS = arc of y. 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y + y = x + 2y 
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 
 
Solution: 
(i) Steps of Construction : 
 
1. Draw line segment BC of any suitable length. 
 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
anlge x at the points P and Q and arms of the angle y at points R and S and arms 
of the angle z at the points L and M. 
3. From the arc, with centre B, cut 
DE = PQ = arc of x, EF = RS = arc of y and FG = LM = arc of z. 
4. Join BG and produce it upto A. 
Then ?ABC = x + y + z 
(ii) Proceed as in part (i) upto step 2. 
3. From the arc, with centre B, cut 
 
DE = 2PQ = 2 arc of x 
EF = RS = arc of y 
FG = LM = arc of z 
4. Join BG and produce it upto point A 
Then ?ABC = 2x + y + z 
(iii) proceed as in (i) upto step 2 
Page 5


18. Constructions 
(Using ruler and compass only) 
EXERCISE 18(A) 
Question 1. 
Given below are the angles x and y. 
 
Without measuring these angles, construct : 
(i) ?ABC = x + y 
(ii) ?ABC = 2x + y 
(iii) ?ABC = x + 2y 
Solution: 
 
(i) Steps of Construction : 
1. Draw a line segment BC of any suitable length. 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
arc x at points P and Q and arms of angle y at points R and S. 
3. From the arc, with centre B, cut DE = PQ arc of x and EF = RS arc of y 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y 
(ii) Steps of Construction : 
 
Proceed in exactly the same way as in part(i) 
takes DE = PQ = arc of x. 
EF = PQ = arc of x and FG = RS = arc of y. 
Join BG and produce it upto A. 
Thus ?ABC = x + x+ y = 2x + y 
(iii) Steps of Construction : 
 
Proceed in exactly the same way as in (ii) 
taking DE = PQ = arc of x. and EF = RS = arc of y and FG = RS = arc of y. 
4. Join BF and produce upto point A. 
Thus ?ABC = x + y + y = x + 2y 
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 
 
Solution: 
(i) Steps of Construction : 
 
1. Draw line segment BC of any suitable length. 
 
2. With B as centre, draw an arc of any suitable radius. With the same radius, draw 
arcs with the vertices of given angles as centres. Let these arcs cut arms of the 
anlge x at the points P and Q and arms of the angle y at points R and S and arms 
of the angle z at the points L and M. 
3. From the arc, with centre B, cut 
DE = PQ = arc of x, EF = RS = arc of y and FG = LM = arc of z. 
4. Join BG and produce it upto A. 
Then ?ABC = x + y + z 
(ii) Proceed as in part (i) upto step 2. 
3. From the arc, with centre B, cut 
 
DE = 2PQ = 2 arc of x 
EF = RS = arc of y 
FG = LM = arc of z 
4. Join BG and produce it upto point A 
Then ?ABC = 2x + y + z 
(iii) proceed as in (i) upto step 2 
 
3. Here cut arc DE = arc PQ = arc of x arc EF = 2 arc RS = 2 arc of y arc FG = arc LM = 
arc of z. 
4. Join BG and produce it upto A 
5. Then ?ABC = x + 2y + z 
Question 3. 
Draw a line segment BC = 4 cm. Construct angle ABC = 60°. 
Solution: 
Steps of Construction : 
 
1. Draw a line segment BC = 4 cm 
2. With B as centre, draw an arc of any suitable radius which cuts BC at the point D. 
3. With D as centre, and the same radius as in step 2, draw one more arc which cuts 
the previous arc at the point E. 
4. Join BE and produce it to the point A. 
Thus ?ABC = 60°