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Using triangle congruencies, prove why the construction of an angle bisector works.

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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.

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Attn: ≡ means congruent here.