Bd is perpendicular to ac because it comes from a and cuts the ac into two equal halves and since the triangle is isoceles if any lines comes through a and intersects the base into 2 equal halves that must be perpendicular
Because we know that angles ∠BAD and ∠BCD are the same, we can conclude that triangles ΔABD and ΔBCD are congruent. This means that angles ∠BDA and ∠BDC are right angles, and lines BD and AC are congruent.
