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 angle - bisector construction

In a straight - edge and compass construction of an angle bisector, we create arcs from the vertex of the angle (in this case, point A) that intersect the sides of the angle (AB and AC). Then, we create additional arcs from the intersection points of the first - set of arcs with the sides of the angle, and the line connecting the vertex to the intersection of these new arcs is the angle bisector. Here, line EF is constructed as the bisector of angle BAC.

Step2: Analyze other statements

There is no indication from the construction that EF is perpendicular to any of the segments BA, AC, or BD, nor is there any indication that EF is parallel to CD.

Answer:

A. Line EF is the bisector of angle BAC.