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Answer:

BD is perpendicular to AC.

Step-by-step explanation:

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.
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

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