Question

1. this diagram is a straightedge and compass construction. select all true statements. a. line ef is the bisector of angle bac. b. line ef is the perpendicular bisector of segment ba. c. line ef is the perpendicular bisector of segment ac. d. line ef is the perpendicular bisector of segment bd. e. line ef is parallel to line cd.

Explanation:

Step1: Recall straight - edge and compass construction properties

In a typical angle - bisector construction using straight - edge and compass, we create equal arcs from the vertex of the angle and then connect the intersection points of the arcs. Here, by the construction of the circles centered at points on the rays of $\angle BAC$, line $EF$ is the angle - bisector of $\angle BAC$.
For perpendicular bisectors, we would need to construct circles with equal radii centered at the endpoints of a segment and connect the intersection points of the circles. There is no indication that $EF$ is a perpendicular bisector of $BA$, $AC$ or $BD$. Also, there is no construction element to suggest that $EF$ is parallel to $CD$.

Answer:

A. Line $EF$ is the bisector of angle $BAC$.