Question

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

Explanation:

Step1: Recall mid - point property

Since B is the mid - point of $\overline{AC}$, by the definition of a mid - point, $AB = BC$ and $BC=\frac{1}{2}AC$.

Step2: Recall angle - bisector property

$\angle ABC$ is a straight - angle ($180^{\circ}$). Since $\angle ABD = 90^{\circ}$ and $\angle DBC=90^{\circ}$, ray $BD$ bisects $\angle ABC$.

Answer:

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