Question

question 2, 5-2 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 equal arcs from the vertex of the angle and then connect the intersection of the arcs with the vertex. Here, line EF is constructed in a way that it divides angle BAC into two equal angles. So, line EF is the bisector of angle BAC.

Step2: Analyze perpendicular - bisector properties

There is no indication from the construction that EF is perpendicular to BA, AC or parallel to CD. However, by the properties of the construction, we can show that EF is the perpendicular bisector of the segment BD. When we construct the angle bisector using the standard straight - edge and compass method, the line joining the intersection points of the arcs (EF) is the perpendicular bisector of the segment joining the points where the initial arcs intersect the sides of the angle (BD).

Answer:

A. Line EF is the bisector of angle BAC.
D. Line EF is the perpendicular bisector of segment BD.