point b is the midpoint of $\overline{ac}$. which statements about the figure must be true? select three options. $\square$ $\angle dbc$ is bisected by ray bd. $\square$ $\angle abc$ is bisected by ray bd. $\square$ $bc = \frac{1}{2}ac$ $\square$ $\overline{db} \cong \overline{bc}$ $\square$ $2m\angle dbc = m\angle abc$

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# Brief Explanations:
1. Analyze each option:
   - Option 1: ∠DBC is an angle, and ray BD is one of its sides, so it can't bisect ∠DBC. Eliminate this.
   - Option 2: Since ∠ABC is a straight angle (180°) and BD is perpendicular to AC (right angle), BD splits ∠ABC into two 90° angles, so it bisects ∠ABC. This is true.
   - Option 3: B is the midpoint of AC, so by midpoint definition, $ BC=\frac{1}{2}AC $. This is true.
   - Option 4: There's no information to suggest $ \overline{DB}\cong\overline{BC} $. Eliminate this.
   - Option 5: ∠DBC is 90°, ∠ABC is 180°, so $ 2m\angle DBC = 2\times90° = 180°=m\angle ABC $. This is true.
# Answer:
B. $ \angle ABC $ is bisected by ray BD,
C. $ BC = \frac{1}{2}AC $,
E. $ 2m\angle DBC = m\angle ABC $

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