Question

which statement is true about the given information?
bd = 1/2 bc
dc = 1/2 be
bd ≅ ce
bc ≅ bd

Explanation:

Step1: Analyze line - segment lengths

From the figure, assume the lengths of the segments formed by the points \(B\), \(C\), \(D\), and \(E\) on the line. Let's consider the relationships between the line - segments.

Step2: Check each option

1. For \(BD=\frac{1}{2}BC\), from the figure, \(BD = BC + CD\), so \(BD>\ BC\), and \(BD

eq\frac{1}{2}BC\).

1. For \(DC=\frac{1}{2}BE\), there is no indication from the figure that \(DC\) is half of \(BE\).
2. For \(\overline{BD}\cong\overline{CE}\), assume \(BC = CD=DE\). Then \(BD=BC + CD\) and \(CE=CD + DE\). Since \(BC = DE\) (by assumption of equal - length sub - segments), we have \(BD = CE\), so \(\overline{BD}\cong\overline{CE}\).
3. For \(\overline{BC}\cong\overline{BD}\), since \(BD=BC + CD\), \(BD>BC\), so \(\overline{BC}\) is not congruent to \(\overline{BD}\).

Answer:

\(\overline{BD}\cong\overline{CE}\)