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Math Question

Consider the following diagram. In the above bridge, \( \overline{\mathrm{BD}} \) is the perpendicular bisector of \( \overline{A C} \). For the bridge to be safe, \( \triangle A B D \cong \triangle C B D \). Considering strictly the information that was given, what sequence of reasons can you use to prove that \( \triangle A B D \) and \( \triangle C B D \) are congruent? (A) \( \angle A \cong \angle C \) (Third Angle Theorem) and \( \triangle A B D \cong \triangle C B D \) (ASA) (B) \( \overline{A D} \cong \overline{C D}(C P C T C) \) and \( \triangle A B D \cong \triangle C B D \) (SSS) (C) \( \overline{B D} \cong \overline{B D} \) (Reflexive Property) and \( \triangle A B D \cong \triangle C B D \) (SAS) (D) \( \angle A D B \cong \angle C D B \) (Corresponding Angles Theorem) and \( \triangle A B D \cong \triangle C B D \) (ASA)

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