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 straightedge - compass construction properties

In a straightedge - compass construction of an angle bisector, we use the intersection of circles centered at the vertex of the angle and points on the rays of the angle. Here, the construction shows the typical way to construct the bisector of $\angle BAC$. The line $EF$ is constructed in a way that it divides $\angle BAC$ into two equal - angles.

Step2: Analyze perpendicular bisector properties

There is no indication from the construction that $EF$ is the perpendicular bisector of $BA$, $AC$, or $BD$. The construction does not follow the steps for constructing a perpendicular bisector of these segments. Also, there is no evidence that $EF$ is parallel to $CD$.

Answer:

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