We are asked to find the length of JL. Let's consider the diagram.
As we can see, JL consists of two segments: JM and ML. Therefore, by the Segment Addition Postulate its length equals the sum of these segment lengths.
JL= JM+ ML
The measure of JM is known from the diagram. How can we find the measure of ML? From the diagram, we see that segments JK and KL have the same length. This means point K is equidistant from J and L. Let's now use the Converse of the Perpendicular Bisector Theorem.
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
According to this theorem, MK is the perpendicular bisector of JL. Therefore, M is the midpoint of JL. We conclude that the length of ML is also 6. Finally, we can substitute JM with 6 and ML with 6 in the equation to calculate JL.
JL&= 6+ 6
&=12
