Question

1. given: (overline{de}) is the perpendicular bisector of (overline{jl}). which statement is not necessarily true?

k is the mid - point of (overline{jl})
(overline{de}perpoverline{jl})
dk = ke
dj = dl

Explanation:

Step1: Recall properties of perpendicular bisector

A perpendicular bisector of a line segment $\overline{JL}$ is a line that is perpendicular to $\overline{JL}$ and passes through its mid - point. If $\overline{DE}$ is the perpendicular bisector of $\overline{JL}$, then the mid - point of $\overline{JL}$ is $K$ (by definition of perpendicular bisector), so $K$ is the mid - point of $\overline{JL}$ and $\overline{DE}\perp\overline{JL}$. Also, any point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment. So $DJ = DL$.

Step2: Analyze each option

The fact that $K$ is the mid - point of $\overline{JL}$ is true by the definition of a perpendicular bisector. $\overline{DE}\perp\overline{JL}$ is also true by the definition of a perpendicular bisector. And $DJ = DL$ because $D$ lies on the perpendicular bisector of $\overline{JL}$. However, there is no information given that would imply $DK=KE$. Just because $\overline{DE}$ is the perpendicular bisector of $\overline{JL}$ does not mean that $K$ bisects $\overline{DE}$.

Answer:

$DK = KE$