in paragraph or two column proof
Using triangle congruencies, prove why the construction of an angle bisector works.
Hint: Draw OA = OB. Then at A and B draw two arcs with the same radius such that the two arcs intersect at D. Since OA = OB, AD = BD (same radius) and OD = OC (reflexive property), triangle OAD ≡ triangle OBD (SSS). Therefore, angle AOD ≡ angle BOD (CPCTC). So, OD is the angle bisector of angle AOB.
Attn: ≡ means congruent here.