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

Steps of construction
(i) Draw a ray AB at the point A.
(ii) Taking A as centre and a convenient radius, draw an arc which intersect AB at C.
(iii) Taking C as centre and with the same radius, draw an arc which intersect the previous arc at D.
(iv) Similarly, taking D as centre, draw arcs with the same radius, draw an arc which intersects at E.
(v) taking D and E as centre, draw arcs with equal radius (more than half of DE), Which intersect at F.
(vi) From the point A, draw a ray AF, which intersects arc DE at G.
(vii) Taking C and G as centre. Draw arcs with equal radius (more than half of CG), which intersect at H.
(viii) From the point A, draw a ray of 45°.
Justification: Join GH and CH.
In ΔAGH and ΔACH,
GH = CH [∵ Arcs of equal radii]
AG = AC [∵ Radii of same circle]
AH = AH [∵ Common]
So, ΔAGH ≅ ΔACH [∵ SSS Congruency rule]
∠GAH = ∠CAH [∵ CPCT]
Hence, ∠GAH = ∠CAH = 45°