Question

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:

• Option A: In a straightedge and compass construction for angle bisector, the steps don't match EF's role here. EF is not an angle bisector of ∠BAC.
• Option B: For perpendicular bisector of BA, the construction would require equidistant from B and A, but EF doesn't satisfy that for BA.
• Option C: Similarly, EF is not the perpendicular bisector of AC as it doesn't meet the criteria for bisecting and being perpendicular to AC.
• Option D: In the construction, the circles centered at B and D (or related) would make EF equidistant from B and D and perpendicular, so EF is the perpendicular bisector of BD.
• Option E: There's no indication of parallelism; EF and CD have no parallel - related construction or properties here.

Answer:

D. Line EF is the perpendicular bisector of segment BD.