Question

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) (2mangle dbc = mangle abc)

Explanation:

Step1: Analyze each option

• Option 1: ∠DBC is bisected by ray BD. A ray can't bisect the angle it's a side of (BD is a side of ∠DBC), so this is false.
• Option 2: ∠ABC is a straight angle (180°) and BD is perpendicular to AC (right angle symbol), so BD splits ∠ABC into two 90° angles, bisecting it. True.
• Option 3: B is the midpoint of AC, so \( BC=\frac{1}{2}AC \). True.
• Option 4: \( \overline{DB} \) is a vertical segment, \( \overline{BC} \) is horizontal; we don't know their lengths are equal. False.
• Option 5: ∠DBC is 90°, ∠ABC is 180°, so \( 2m\angle DBC = 2\times90° = 180° = m\angle ABC \). True.

Answer:

• ∠ABC is bisected by ray BD.
• \( BC = \frac{1}{2}AC \)
• \( 2m\angle DBC = m\angle ABC \)