Question

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

Explanation:

Step1: Analyze segment lengths

From the figure, \(BD = BC + CD\), so \(BC
eq BD\) and \(BD
eq\frac{1}{2}BC\). Also \(BC
eq\frac{1}{2}BE\) as \(BE=BC + CD+DE\). And since \(BC = CD=DE\), \(BD = 2BC\) and \(CE = 2CD\), so \(BD = CE\) (i.e., \(\overline{BD}\cong\overline{CE}\)).

Answer:

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