Question

if \\(\overline{bc} \cong \overline{cd}\\) and \\(de = 66\\), what is \\(be\\)?
\\(be = \square\\)

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \( \overline{BC}\cong\overline{CD}\), \( \angle BEC=\angle DEC = 90^{\circ}\) (given the right - angle at \(E\)), and \( \overline{CE}\cong\overline{CE}\) (common side). By the HL (Hypotenuse - Leg) Congruence Theorem for right - triangles (\(\triangle BEC\) and \(\triangle DEC\)), \(\triangle BEC\cong\triangle DEC\).

Step2: Use the property of congruent triangles

If two triangles are congruent (\(\triangle BEC\cong\triangle DEC\)), then their corresponding sides are equal. That is, \(BE = DE\).

Answer:

\(66\)