Points C and D lie on opposite sides of line AB so that AD = AC, BD = BC Prove that AB is the bisector of angle DAC.

Triangles ABC and ABD are equal in the third sign of equality of triangles: on three sides. By condition AD = AC; BC = BD; side AB – common. Hence, the angle CAB = angle BAD,

that is, AB is the bisector of the angle DAC.

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