Question

to construct a line passing through point c that is parallel to the line ab, han constructed the perpendicular bisector of segment ab and then drew line cd. his work is shown here. is line cd guaranteed to be parallel to line ab? explain how you know.

Explanation:

The construction of the perpendicular - bisector of segment \(AB\) and then drawing line \(CD\) does not guarantee parallelism. For two lines to be parallel, we need to use properties like equal corresponding angles or equal alternate - interior angles formed by a transversal. In this construction, there is no relation established between the angles formed by a transversal with \(AB\) and \(CD\) to ensure parallelism.

Answer:

No, line \(CD\) is not guaranteed to be parallel to line \(AB\) because the construction steps do not create the necessary angle relationships (such as equal corresponding or alternate - interior angles) that would ensure parallel lines.