Question

midpoints and bisectors
n exercises 48 and 46, identify the segment bisector of ab. then find ab.
1.
2.

Explanation:

Step1: Recall the property of segment - bisector

A segment bisector divides a line - segment into two equal parts. In both cases, the line \(d\) (in the first figure) and line \(l\) (in the second figure) passing through the mid - point \(M\) of \(\overline{AB}\) are the segment bisectors.

Step2: Calculate the length of \(AB\) for the first case

If \(AM = 15\), since \(M\) is the mid - point of \(\overline{AB}\), then \(AB=2\times AM\). So \(AB = 2\times15=30\).

Step3: Calculate the length of \(AB\) for the second case

If \(AM = 5.5\), since \(M\) is the mid - point of \(\overline{AB}\), then \(AB = 2\times AM\). So \(AB=2\times5.5 = 11\).

Answer:

1. Segment bisector: line \(d\), \(AB = 30\)
2. Segment bisector: line \(l\), \(AB = 11\)