1/3(9x-24) x simplify the expression

Yes, the proof correctly justifies that triangles ABC and DBC are congruent

Step-by-step explanation:

1) The incenter is given by the intersection of three angle bisectors of the three angles of the triangle

Therefore, given that the line BC connects the vertex B to the incenter, we have that BC is an altitude (gives the height of the angle ∠ABD)

2) The segment BC bisects ∠ABD, being that segment BC is an altitude of the angle and also leads to the incenter of the triangle ABD

Therefore, ∠ABC and ∠DBC are congruent by the definition of bisection of ∠ABD

3) Given that triangle ABD is an isosceles triangle, we have segments AB and DB are congruent

4) Segment BC of triangles ABC and DBC is congruent to itself by reflexive property

5) Therefore, as obtained above, segment AB, ∠ABC, and segment BC of triangle ΔABC are congruent to the corresponding segment BD, ∠DBC, and segment BD of triangle ΔDBC, we have that ΔABC and ΔDBC are congruent by Side-Angle-Side rule of congruency