Question

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

Explanation:

Step1: Analyze the segments

From the figure, we can see that \(BC = CD = DE\). So \(BE=BC + CD+DE = 3BC\), \(BD = BC + CD=2BC\).

Step2: Check each option

• Option 1: \(BC\cong BD\) is false since \(BD = 2BC\).
• Option 2: \(BD\cong CE\) is false. \(CE=CD + DE = 2BC\), \(BD = 2BC\), but they are not congruent in the sense of segment congruence (they are equal in length but not the same segment).
• Option 3: \(BC=\frac{1}{2}BE\) is false. Since \(BE = 3BC\), \(BC=\frac{1}{3}BE\).
• Option 4: \(BD = 2BC\) is true.

Answer:

\(BD = 2BC\) (the fourth option)