Question

the diagram below is a straightedge and compass construction. select both true statements. line ef is the angle bisector of angle bac. line ef is the perpendicular bisector of segment ba. line ef is the perpendicular bisector of segment ac. line ef is the perpendicular bisector of segment bd. line ef is parallel to line cd.

Explanation:

1. For "Line EF is the angle bisector of angle BAC": In a straightedge and compass construction for angle bisector, the construction of EF (from the intersection of circles) would bisect ∠BAC. So this is true.
2. For "Line EF is the perpendicular bisector of segment BD": The circles centered at B and D (or related centers) would have EF as the perpendicular bisector since the intersection of two circles' centers' line and the common chord (BD) is perpendicular bisected by EF. So this is true.
3. The other statements:

• "Line EF is the perpendicular bisector of segment BA": EF does not bisect BA perpendicularly as per the construction.
• "Line EF is the perpendicular bisector of segment AC": EF is not related to bisecting AC perpendicularly.
• "Line EF is parallel to line CD": There's no indication of parallelism from the construction.

Answer:

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