Courses

# NCERT Solution - Constructions Class 9 Notes | EduRev

## Class 9 : NCERT Solution - Constructions Class 9 Notes | EduRev

``` Page 1

Cbse-spot.blogspot.com
1

Class IX  Chapter 11 – Constructions
Maths

Exercise 11.1 Question
1:
Construct an angle of 90° at the initial point of a given ray and justify the construction.
The below given steps will be followed to construct an angle of 90°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU, which is the required ray making 90° with the given ray PQ.
Page 2

Cbse-spot.blogspot.com
1

Class IX  Chapter 11 – Constructions
Maths

Exercise 11.1 Question
1:
Construct an angle of 90° at the initial point of a given ray and justify the construction.
The below given steps will be followed to construct an angle of 90°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU, which is the required ray making 90° with the given ray PQ.
Cbse-spot.blogspot.com
2

Justification of Construction:
We can justify the construction, if we can prove UPQ = 90°.
For this, join PS and PT.

We have,  SPQ =  TPS = 60°. In (iii) and (iv) steps of this construction, PU was
drawn as the bisector of  TPS.
UPS =  TPS
Also, UPQ = SPQ + UPS
= 60° + 30°
= 90°
Question 2:
Construct an angle of 45° at the initial point of a given ray and justify the construction.
?
Page 3

Cbse-spot.blogspot.com
1

Class IX  Chapter 11 – Constructions
Maths

Exercise 11.1 Question
1:
Construct an angle of 90° at the initial point of a given ray and justify the construction.
The below given steps will be followed to construct an angle of 90°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU, which is the required ray making 90° with the given ray PQ.
Cbse-spot.blogspot.com
2

Justification of Construction:
We can justify the construction, if we can prove UPQ = 90°.
For this, join PS and PT.

We have,  SPQ =  TPS = 60°. In (iii) and (iv) steps of this construction, PU was
drawn as the bisector of  TPS.
UPS =  TPS
Also, UPQ = SPQ + UPS
= 60° + 30°
= 90°
Question 2:
Construct an angle of 45° at the initial point of a given ray and justify the construction.
?
Cbse-spot.blogspot.com
3

The below given steps will be followed to construct an angle of 45°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU. Let it intersect the arc at point V.
(vi) From R and V, draw arcs with radius more than RV to intersect each other at W.
Join PW.
PW is the required ray making 45° with PQ.

Justification of Construction:
We can justify the construction, if we can prove WPQ = 45°.
For this, join PS and PT.
Page 4

Cbse-spot.blogspot.com
1

Class IX  Chapter 11 – Constructions
Maths

Exercise 11.1 Question
1:
Construct an angle of 90° at the initial point of a given ray and justify the construction.
The below given steps will be followed to construct an angle of 90°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU, which is the required ray making 90° with the given ray PQ.
Cbse-spot.blogspot.com
2

Justification of Construction:
We can justify the construction, if we can prove UPQ = 90°.
For this, join PS and PT.

We have,  SPQ =  TPS = 60°. In (iii) and (iv) steps of this construction, PU was
drawn as the bisector of  TPS.
UPS =  TPS
Also, UPQ = SPQ + UPS
= 60° + 30°
= 90°
Question 2:
Construct an angle of 45° at the initial point of a given ray and justify the construction.
?
Cbse-spot.blogspot.com
3

The below given steps will be followed to construct an angle of 45°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU. Let it intersect the arc at point V.
(vi) From R and V, draw arcs with radius more than RV to intersect each other at W.
Join PW.
PW is the required ray making 45° with PQ.

Justification of Construction:
We can justify the construction, if we can prove WPQ = 45°.
For this, join PS and PT.
Cbse-spot.blogspot.com
4

We have,  SPQ =  TPS = 60°. In (iii) and (iv) steps of this construction, PU was
drawn as the bisector of  TPS.
?

?
UPS =

TPS
Also, UPQ = SPQ + UPS
= 60° + 30°
= 90°
In step (vi) of this construction, PW was constructed as the bisector of  UPQ.
WPQ =  UPQ
Question 3:
Construct the angles of the following measurements:
(i) 30° (ii) (iii) 15° Answer:
(i)30°
The below given steps will be followed to construct an angle of 30°.
Step I: Draw the given ray PQ. Taking P as centre and with some radius, draw an arc
of a circle which intersects PQ at R.
Step II: Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at point S.
?
?
Page 5

Cbse-spot.blogspot.com
1

Class IX  Chapter 11 – Constructions
Maths

Exercise 11.1 Question
1:
Construct an angle of 90° at the initial point of a given ray and justify the construction.
The below given steps will be followed to construct an angle of 90°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU, which is the required ray making 90° with the given ray PQ.
Cbse-spot.blogspot.com
2

Justification of Construction:
We can justify the construction, if we can prove UPQ = 90°.
For this, join PS and PT.

We have,  SPQ =  TPS = 60°. In (iii) and (iv) steps of this construction, PU was
drawn as the bisector of  TPS.
UPS =  TPS
Also, UPQ = SPQ + UPS
= 60° + 30°
= 90°
Question 2:
Construct an angle of 45° at the initial point of a given ray and justify the construction.
?
Cbse-spot.blogspot.com
3

The below given steps will be followed to construct an angle of 45°.
(i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre,
which intersects PQ at R.
(ii) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(iii) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(iv) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(v) Join PU. Let it intersect the arc at point V.
(vi) From R and V, draw arcs with radius more than RV to intersect each other at W.
Join PW.
PW is the required ray making 45° with PQ.

Justification of Construction:
We can justify the construction, if we can prove WPQ = 45°.
For this, join PS and PT.
Cbse-spot.blogspot.com
4

We have,  SPQ =  TPS = 60°. In (iii) and (iv) steps of this construction, PU was
drawn as the bisector of  TPS.
?

?
UPS =

TPS
Also, UPQ = SPQ + UPS
= 60° + 30°
= 90°
In step (vi) of this construction, PW was constructed as the bisector of  UPQ.
WPQ =  UPQ
Question 3:
Construct the angles of the following measurements:
(i) 30° (ii) (iii) 15° Answer:
(i)30°
The below given steps will be followed to construct an angle of 30°.
Step I: Draw the given ray PQ. Taking P as centre and with some radius, draw an arc
of a circle which intersects PQ at R.
Step II: Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at point S.
?
?
Cbse-spot.blogspot.com
5

Step III: Taking R and S as centre and with radius more than RS, draw arcs to
intersect each other at T. Join PT which is the required ray making 30° with the

The below given steps will be followed to construct an angle of .
(1) Take the given ray PQ. Draw an arc of some radius, taking point P as its centre,
which intersects PQ at R.
(2) Taking R as centre and with the same radius as before, draw an arc intersecting
the previously drawn arc at S.
(3) Taking S as centre and with the same radius as before, draw an arc intersecting
the arc at T (see figure).
(4) Taking S and T as centre, draw an arc of same radius to intersect each other at U.
(5) Join PU. Let it intersect the arc at point V.
(6) From R and V, draw arcs with radius more than RV to intersect each other at W.
Join PW.
(7) Let it intersect the arc at X. Taking X and R as centre and radius more than

given ray PQ.

(   ii   )
```
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;