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Construct an angle of 90 0 at the initial point of a given ray and justify the construction.
Asked by Tanvi Last Modified
Answer 
Tasneem
The steps required to construct an angle of 90° is as follows.
(i)Consider the given ray PQ. Draw an arc of some radius making point P as its centre, which intersects PQ at R.
(ii) Now, taking R as centre with the same radius as before, draw an arc intersecting the previously drawn arc at S.
(iii) Mark S as centre 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.
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°
read less 
SPQ = TPS = 60o. In (iii) and (iv) steps of this construction, we have drawn PU as the bisector of TPS.
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