NCERT solution Class 9 constructions

NCERT Solutions

Class 9 Maths

Constructions

NCERT Questions

Ex.11.1 Q.1
Ex.11.1 Q.2
Ex.11.1 Q.3
Ex.11.1 Q.4
Ex.11.1 Q.5
Ex.11.1 Q.6
Ex.11.2 Q.2
Ex.11.2 Q.3
Ex.11.2 Q.4
Ex.11.2 Q.5

Ex.11.1 Q.2

Construct an angle of 45⁰ at the initial point of a given ray and justify the construction.

The below given steps will be followed to construct an angle of 45⁰.

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.

4. Taking S and T as centre, draw an arc of same radius to intersect each other at U.

5. From R and V, draw arcs with radius more than RV/2 to intersect each other at W.

Join PW.

PW is the required ray making 45⁰ with PQ.

Justification of Construction:

We can justify the construction, if we can prove ∠WPQ = 45⁰.

For this, join PS and PT.

We have, ∠SPQ = ∠TPS = 60⁰.

In 3 and 4 steps of this construction, PU was drawn as the bisector of ∠TPS.

So, ∠UPS = ∠TPS ÷ 2 = 60⁰ ÷ 2 = 30⁰

Also, ∠UPQ = ∠SPQ + ∠UPS

In step (vi) of this construction, PW was constructed as the bisector of ∠UPQ.

So, ∠WPQ = ∠UPQ ÷ 2 = 90⁰ ÷ 2 = 45⁰

Video solution:

Constructions Class 9 Maths NCERT Chapter 11 NCERT Solutions

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NCERT solutions of Constructions Class 9 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 9 Maths Constructions NCERT solutions.