Math, asked by shivanshgilra28, 5 months ago

1. Construct an angle of 45° at the initial point of a given ray and justify the construction​

Answers

Answered by Ranveerx107
0

Question:-

Construct an angle of 45° at the initial point of a given ray and justify the construction.:-

Answer:-

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

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

(vi) 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 45° with PQ.

Justification of Construction:-

We can justify the construction, if we can prove ∠WPQ = 45°.

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.

So, ∠UPS = ∠TPS/2 = 60°/2 = 30°

Also, ∠UPQ = ∠SPQ + ∠UPS

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

So, ∠WPQ = ∠UPQ/2 = 90°/2 = 45°

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