Answer to Question #138117 in Geometry for J

Question

Prove that the compass and straightedge construction for an angle bisector is valid.

Answer 1

In triangles OAD and OBD,

OA=OB being radii of same circle.

AD=BD being radii of same circle

OD common side. Hence by S-S-S congruency the triangles are congruent. Hence the corresponding angles are equal. In other words, $\angle AOD=\angle BOD.$ So bijection by straight edge and compass is justified.