i cant continue to write my proof.Ok triangle ABC is congruent to triangle A'B'C'. Segment AD bisects angle BAC
and segment A'D' bisects angle B'A'C'. Proof segment AD is congruent to A'D'.
Because triangle ABC is congruent to triangle A'B'C' (given)
so angle BAC = angle B'A'C' angle BCA = angle B'C'A'$$\Rightarrow$$ angle DCA = angle D'C'A' (corresponding angles of two congruent triangles are equal)
and segment AC = segment A'C' (corresponding sides of two congruent triangles are equal)
because AD bisects angle BAC (given)
so angle BAD = angle CAD =1/2 angle BAC (angle bisect theorem)
same, angle B'A'D' = angle C'A'D' =1/2 angle B'A'C'
because angle BAC = angle B'A'C' (proved)
1/2 angle BAC =1/2 angle B'A'C $$\Rightarrow$$ angle DAC =angle D'A'C'
In the triangle DCA and triangle D‘C'A'
angle DAC =angle D'A'C'
segment AC = segment A'C'
angle DCA = angle D'C'A'
so triangle DCA congruent to triangle D‘C'A' (ASA) (angle -side-angle )
so segment AD is congruent to segment A'D' (corresponding sides of two congruent triangles are equal)I
i wish that work. And left side the image have something wrong. i am really sorry. Thank you!