Question

point b is the midpoint of $overline{ac}$. which statements about the figure must be true? choose three correct answers. $angle abc$ is bisected by ray bd. $overline{db}congoverline{bc}$. $angle dbc$ is bisected by ray bd. $bc = \frac{1}{2}ac$. $2mangle dbc = mangle abc$

Explanation:

Step1: Recall mid - point property

Since B is mid - point of AC, $BC=\frac{1}{2}AC$.

Step2: Analyze angle bisection

Ray BD divides $\angle DBC$ into two equal angles, so $\angle DBC$ is bisected by ray BD.

Step3: Check other statements

There's no info to support $\angle ABC$ is bisected by BD or $\overline{DB}\cong\overline{BC}$.

Answer:

$\angle DBC$ is bisected by ray BD., $BC = \frac{1}{2}AC$