Final answer:
The statement is justified by the fact that AD bisects angle BAC into two congruent angles BAD and CAD because AD is perpendicular to BC. This leads to the congruency of triangles ABD and ACD through the ASA postulate, resulting in the angles B and C being congruent.
Step-by-step explanation:
The reason that justifies the statement 'angle BAD is congruent to angle CAD' when segment AD is perpendicular to segment BC is that AD bisects the angle BAC. This happens because when a line is perpendicular to another line, it creates two right angles, and if that line is also a bisector, it splits the right angle into two congruent angles. Therefore, in this case, AD bisects angle BAC and creates two congruent angles, BAD and CAD.
Now, given that AB ≅ AC and AD bisects angle BAC, creating two congruent angles (∠BAD ≅ ∠CAD), we can use the Angle-Side-Angle (ASA) postulate to prove that triangles ABD and ACD are congruent. Since angles ∠BAD and ∠CAD are congruent (given reason), AD is a common side, and AB ≅ AC (given), triangle ABD ≅ triangle ACD by ASA postulate. And through the congruency of these triangles, it follows that ∠B ≅ ∠C.