Question

which figure shows the geometric construction of an angle bisector?

Explanation:

Step1: Recall angle - bisector construction

To construct an angle bisector, we start with an angle $\angle AOB$. We use a compass to draw arcs from the vertex $O$ that intersect the sides of the angle at points $A$ and $B$. Then, from points $A$ and $B$, we draw arcs of equal radius inside the angle that intersect at a point $C$. The ray $OC$ is the angle - bisector of $\angle AOB$.

Step2: Analyze the figures

In figure A, it shows the construction of an equilateral triangle (two intersecting circles with equal radii centered at two endpoints of a line - segment). In figure B, it shows the correct steps of constructing an angle bisector. We have an angle $\angle AOB$, arcs are drawn from $O$ to intersect the sides of the angle, and then another set of arcs from the intersection points on the sides of the angle to find the point $C$ such that $\overrightarrow{OC}$ bisects $\angle AOB$.

Answer:

B. The figure with angle $\angle AOB$ and ray $\overrightarrow{OC}$ bisecting it.