Question

if \\(overline{bc} \cong \overline{cd}\\) and \\(ad = 67\\), what is \\(bd\\)?
\\(bd = \square\\)

Explanation:

Step1: Identify the perpendicular bisector

Since \( AC \perp BD \) (right angle at \( A \)) and \( BC \cong CD \), \( AC \) is the perpendicular bisector of \( BD \). So, \( AB = AD \) and \( BD = 2 \times AD \).

Step2: Calculate \( BD \)

Given \( AD = 67 \), then \( BD = 2 \times 67 = 134 \).

Answer:

\( 134 \)