Given triangle ABC, (as shown in the diagram attached) the sides AC and CB are congruent.
Also line CD bisects line AB.
Therefore, line
[tex]\begin{gathered} AD\cong BD \\ Angle\text{ bisector of a triangle} \\ An\text{ angle bisector of a triangle divides the opposite side into two} \\ \text{segments that are prportional }to\text{ the other two sides of the triangle} \\ \text{Hence, if CD bisects line AB, and AC}\cong BC \\ \text{Then AB}\cong BD \end{gathered}[/tex][tex]\begin{gathered} \angle ACD=\angle BCD \\ \text{Angle bisector} \\ \text{If the line CD bisects line AB, and }AD\cong BD \\ \text{Then }\angle ACD\cong\angle BCD \end{gathered}[/tex]Therefore, in both triangles, we have;
[tex]AC\cong CB\text{ (Given)}[/tex][tex]AD\cong BD\text{ (Angle bisector)}[/tex][tex]undefined[/tex]