Final answer:
Without additional information or a diagram, we cannot conclude which lines are parallel or perpendicular. The congruence of segments suggests a symmetry that might point towards an isosceles or equilateral triangle, but no inherent perpendicularity.
Step-by-step explanation:
The given statements do not directly suggest any information about lines being parallel or perpendicular. Without a diagram or additional context, we cannot infer the relationships between AC, BD, AD, and BC just from the given information. For a complete analysis, we require additional theorems or properties relating to the lines and points described.
However, if we assume that AB, BC, and AC are sides of a triangle ABC, and BD is a line segment connecting a vertex B to a point D such that AB and BD are congruent, then one possibility is that ABC is an isosceles triangle where AB equals BC. If BD is congruent to AB, and B is the midpoint of AC, then the triangle is also equilateral if we assume that BD is also congruent to BC. An equilateral triangle does not have any perpendicular sides inherently unless additional criteria are specified.