Question

which statement is true about the given information?
diagram: line segment with points b, c, d, e (b---c---d---e) and tick marks indicating congruent segments between b-c, c-d, d-e
options:
bd = \\(\frac{1}{2}\\)bc
bc = \\(\frac{1}{2}\\)be
\\(\overline{bd} \cong \overline{ce}\\)
\\(\overline{bc} \cong \overline{bd}\\)

Explanation:

Step1: Analyze segment markings

The number line has equal markings, so \( BC = CD = DE \). Let \( BC = x \), then \( CD = x \), \( DE = x \).

Step2: Evaluate each option

• Option 1: \( BD = BC + CD = x + x = 2x \), \( \frac{1}{2}BC=\frac{x}{2} \), so \( BD

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

• Option 2: \( BE = BC + CD + DE = 3x \), \( \frac{1}{2}BE=\frac{3x}{2} \), \( BC = x

eq\frac{3x}{2} \).

• Option 3: \( BD = BC + CD = 2x \), \( CE = CD + DE = 2x \), so \( \overline{BD}\cong\overline{CE} \) (equal length).
• Option 4: \( BC = x \), \( BD = 2x \), so \( \overline{BC}

ot\cong\overline{BD} \).

Answer:

\( \overline{BD}\cong\overline{CE} \) (the third option)