Question

which statement is true about the given information?
bd = \frac{1}{2}bc
bc = \frac{1}{2}be
\overline{bd} \cong \overline{ce}
\overline{bc} \cong \overline{bd}

Explanation:

Step1: Analyze the segments

Assume the length of each small segment (between \(B - C\), \(C - D\), \(D - E\)) is \(x\).

Step2: Calculate lengths

• \(BD=BC + CD=x + x = 2x\), \(BC=x\), so \(BD

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

• \(BE=BC + CD+DE=x + x+x = 3x\), \(BC=x\), so \(BC

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

• \(BD = 2x\), \(CE=CD + DE=x + x = 2x\), so \(\overline{BD}\cong\overline{CE}\) (by the definition of congruent segments, segments with equal length are congruent).
• \(BC=x\), \(BD = 2x\), so \(\overline{BC}

ot\cong\overline{BD}\).

Answer:

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