Question

1. match the correct answers.

given: \\( \triangle a b c \\); ray \\( \overrightarrow{d b} \\) is the perpendicular bisector of \\( \overline{a c} ; a b=12 \\) in

what is the length of \\( \overline{c b} \\) ?

by what theorem?

1. match the correct answers.

Explanation:

Step1: Recall the Perpendicular Bisector Theorem

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
In \(\triangle ABC\), ray \(\overrightarrow{DB}\) is the perpendicular bisector of \(\overline{AC}\). Point \(B\) is on the perpendicular bisector of \(\overline{AC}\).

Step2: Apply the theorem

Since \(AB = 12\) in and by the Perpendicular Bisector Theorem \(CB=AB\) (because \(B\) is on the perpendicular bisector of \(AC\)).

Answer:

Length of \(\overline{CB}\): \(12\) inches.
Theorem: Perpendicular Bisector Theorem.